stern-gottfried - travelling fires for structural design€¦ · stern-gottfried under the...

186
Travelling Fires for Structural Design Jamie Stern-Gottfried A thesis submitted for the degree of Doctor of Philosophy The University of Edinburgh 2011

Upload: others

Post on 17-Apr-2020

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

Travelling Fires for

Structural Design

Jamie Stern-Gottfried

A thesis submitted for the degree of

Doctor of Philosophy

The University of Edinburgh

2011

Page 2: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed
Page 3: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

i

To my wife, Ina

Page 4: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

ii

Page 5: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

iii

Abstract

Traditional methods for specifying thermal inputs for the structural fire analysis of

buildings assume uniform burning and homogeneous temperature conditions

throughout a compartment, regardless of its size. This is in contrast to the

observation that accidental fires in large, open-plan compartments tend to travel

across floor plates, burning over a limited area at any one time.

This thesis reviews the assumptions inherent in the traditional methods and

addresses their limitations by proposing a methodology that considers travelling

fires for structural design. Central to this work is the need for strong collaboration

between fire safety engineers to define the fire environment and structural fire

engineers to assess the subsequent structural behaviour.

The traditional hypothesis of homogeneous temperature conditions in post-

flashover fires is reviewed by analysis of existing experimental data from well-

instrumented fire tests. It is found that this assumption does not hold well and that

a rational statistical approach to fire behaviour could be used instead.

The methodology developed in this thesis utilises travelling fires to produce more

realistic fire scenarios in large, open-plan compartments than the conventional

methods that assume uniform burning and homogeneous gas phase temperatures

which are only applicable to small compartments. The methodology considers a

family of travelling fires that includes the full range of physically possible fire sizes

Page 6: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

iv

within a given compartment. The thermal environment is split into two regions: the

near field (flames) and the far field (smoke away from the flames). Smaller fires

travel across a floor plate for long periods of time with relatively cool far field

temperatures, while larger fires have hotter far field temperatures but burn for

shorter durations.

The methodology is applied to case studies showing the impact of travelling fires on

generic concrete and steel structures. It is found that travelling fires have a

considerable impact on the performance of these structures and that conventional

design approaches cannot automatically be assumed to be conservative. The results

indicate that medium sized fires between 10% and 25% of the floor area are the most

onerous for a structure. Detailed sensitivity analyses are presented, showing that the

structural design and fuel load have a larger impact on structural behaviour than

any numerical or physical parameter required for the methodology.

This thesis represents a foundation for using travelling fires for structural analysis

and design. The impact of travelling fires is critical for understanding true structural

response to fire in modern, open-plan buildings. It is recommended that travelling

fires be considered more widely for structural design and the structural mechanics

associated with them be studied in more detail. The methodology presented in this

thesis provides a key framework for collaboration between fire safety engineers and

structural fire engineers to achieve these aims.

Page 7: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

v

Declaration

This thesis and the work described within have been completed solely by Jamie

Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis

Torero. Where others have contributed or other sources are quoted, full references

are given. This work has not been submitted for any other degree or professional

qualification.

Jamie Stern-Gottfried

2011

Page 8: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

vi

Page 9: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

vii

Acknowledgements

Firstly I would like to thank my supervisor, friend, confidant, and certain future

collaborator Guillermo Rein for his constant encouragement, insightful guidance,

and contagious optimism. Our meetings in your office, telephone calls, emails, and

discussions wherever we happened to be were always welcomed and extremely

important for the development of this thesis. I am also grateful for the warm

hospitality you and Cecile have extended to me.

I would also like to thank my second supervisor José Luis Torero for providing

ideas and conversations that helped shape this work. Thank you for developing and

fostering a fantastic research group. It has been a genuine pleasure to be a part of it.

I am extremely grateful for the support of Arup in funding this research and

affording me time away from the office. In particular, thank you to Barbara Lane for

making this all happen and sticking by me through uncertain times. I am thankful

for all the support from my many colleagues past and present who gave their

thoughts on my work and covered for me when I was away, especially Paul,

Gabriele, and Hay Sun. I look forward to applying this work to our projects!

Additional thanks goes to all of the structural fire engineers at Arup and Edinburgh

who helped shed light on the previously dark subject to me of structural

engineering. Specifically, thanks to Graeme, Linus, Darlene, Charlotte, Hélène,

Allan, Sue, Neal, Alex, Susan, and Luke.

Page 10: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

viii

Extra special thanks goes to Angus for not just listening to my thoughts, but

wanting to do something about them! Our collaboration has been extremely

rewarding and fun. I’m pleased that we can keep it up.

Thanks to all of the students and other friendly faces in the fire group at Edinburgh

for some great times and always making me feel welcome. Thanks to Wolfram and

Agustin for the wonderfully geeky fire dynamics conversations. And thanks to

Rorbo for graciously sharing his time with “The Boss” with me when I was in

Edinburgh and helping me navigate the Uni bureaucracy when I was not.

I am very grateful to all my family back in the USA for all you have done for me and

giving me such incredible support from a distance – thank you!

Lastly, and most importantly, thank you Ina. You have been an absolutely

incredible girlfriend, fiancée, and wife throughout this process. You have done so

much for me in terms of all the little things (the Sunday lunch breaks were always

delicious!), but also the big ones. For that I am extremely grateful and incredibly

happy to have you in my life.

Page 11: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

ix

Contents

Abstract ................................................................................................................................. iii

Declaration ............................................................................................................................ v

Acknowledgements ........................................................................................................... vii

Contents ................................................................................................................................ ix

Scholarly Output ............................................................................................................... xiii

Preface ................................................................................................................................ xvii

1 Introduction ......................................................................................................................1

1.1 Traditional Methods ............................................................................................2

1.2 Non-Uniform Burning .........................................................................................4

1.3 Travelling Fires .....................................................................................................5

1.4 A New Methodology ...........................................................................................7

1.5 Collaboration ........................................................................................................8

2 Experimental Review of the Homogeneous Temperature

Assumption in Post-Flashover Compartment Fires ................................................11

2.1 Introduction ........................................................................................................11

2.2 The Homogeneous Temperature Assumption ..............................................12

2.2.1 Origins of the Assumption ................................................................12

2.2.2 Critiques of the Assumption .............................................................14

2.3 Experimental Review ........................................................................................15

2.3.1 Non-Uniform Burning in Experiments ............................................15

2.3.2 Travelling Fires ...................................................................................16

Page 12: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

x

2.3.3 Fire Tests with High Spatial Resolution ......................................... 17

2.3.4 Data Distributions .............................................................................. 25

2.3.5 Standard Deviation vs. Temperature Rise ...................................... 26

2.4 Effect of Temperature Heterogeneity on the Structure ................................ 30

2.5 Conclusions ........................................................................................................ 38

3 A Review of Travelling Fires in Structural Analysis ............................................ 43

3.1 Introduction ........................................................................................................ 43

3.2 Traditional Design Methods ............................................................................ 44

3.3 Limitations of the Uniform Burning Assumption ........................................ 46

3.3.1 Evidence from Experiments ............................................................. 48

3.3.2 Evidence from Accidental Fires ....................................................... 50

3.4 Pioneering Methods .......................................................................................... 51

3.4.1 Large Firecell Method - HERA New Zealand ................................ 51

3.4.2 Travelling Fires Methodology – University of Edinburgh ........... 54

3.5 Structural Response........................................................................................... 62

3.5.1 Steel Frame .......................................................................................... 63

3.5.2 Concrete Frame .................................................................................. 65

3.5.3 Vertically Travelling Fires ................................................................. 67

3.6 Practical Applications ....................................................................................... 69

3.7 Conclusions ........................................................................................................ 73

4 The Influence of Travelling Fires on a Concrete Frame ........................................ 81

4.1 Introduction ........................................................................................................ 81

4.2 Limitations of Current Design Fires ............................................................... 83

4.3 Travelling Fires .................................................................................................. 85

4.3.1 Temperature Definition ..................................................................... 85

4.3.2 Fire Size ............................................................................................... 87

4.4 Structural Failure Criteria ................................................................................ 88

4.5 Structural Modelling ......................................................................................... 89

4.5.1 Structural Arrangement .................................................................... 89

Page 13: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xi

4.6 Base Case Fires ...................................................................................................91

4.6.1 Structural and Thermal Analysis .....................................................93

4.7 Parametric Study ................................................................................................98

4.7.1 Far Field Definition ............................................................................98

4.7.2 Fire Shape and Path ..........................................................................101

4.8 Summary and Concluding Remarks .............................................................103

5 Refinement and Application of the Travelling Fires Methodology ..................109

5.1 Introduction ......................................................................................................109

5.2 Travelling Fires Framework ...........................................................................111

5.3 Analytical Model ..............................................................................................114

5.3.1 Burning Times ...................................................................................114

5.3.2 Near Field vs. Far Field ....................................................................116

5.3.3 Spatial Discretisation ........................................................................120

5.4 Application to a Generic Structure ................................................................124

5.5 Parameter Sensitivity Study ...........................................................................127

5.5.1 Fire Size ..............................................................................................127

5.5.2 Grid Size .............................................................................................130

5.5.3 Rebar Depth .......................................................................................133

5.5.4 Bay Location and Bay Size...............................................................135

5.5.5 Fuel Load Density and Heat Release Rate per Unit Area ...........138

5.5.6 Heat Transfer .....................................................................................139

5.5.7 Near Field Temperature ..................................................................141

5.5.8 Steel Structure ...................................................................................142

5.6 Comparison to Conventional Methods .........................................................146

5.7 Final Remarks ...................................................................................................147

6 Conclusions and Future Work ...................................................................................153

6.1 Conclusions .......................................................................................................153

6.2 Future Work ......................................................................................................155

6.2.1 Fire Environment ..............................................................................156

Page 14: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xii

6.2.2 Fire – Structure Interface ................................................................. 157

6.2.3 Structural Response ......................................................................... 158

Appendix A Heat Transfer Calculations ..................................................................... 163

A.1 Concrete Beam Temperatures ........................................................................ 163

A.2 Unprotected Steel Beam Temperatures ........................................................ 165

A.3 Protected Steel Beam Temperatures ............................................................. 166

Page 15: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xiii

Scholarly Output

Journal Papers

Stern-Gottfried, J., Rein, G., Bisby, L.A., and Torero, J.L., “Experimental review

of the homogeneous temperature assumption in post-flashover compartment

fires”. Fire Safety Journal, Vol. 45, 2010, pp. 249-261.

Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling

fires on a concrete frame”. Engineering Structures, Vol. 33, 2011, pp. 1635-1642.

Invited Talks

“Fires in Large Compartments”, Invited Talk at The Rasbash Lecture, hosted by

The Institution of Fire Engineers, Andover, UK, 2008.

“Design Fires for Structural Analysis”, as part of the workshop on Structural

Fire Engineering prior to The 9th International Symposium on Fire Safety Science in

Karlsruhe, Germany, 2008.

Conference and Magazine Papers

Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "An Innovative Approach

to Design Fires for Structural Analysis of Non-Conventional Buildings: A Case

Study". International Workshop in Applications of Structural Fire Engineering,

Prague, Czech Republic, 2009.

Page 16: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xiv

Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "A Novel Methodology for

Determining Design Fires for Structural Fire Analysis". 6th Mediterranean

Combustion Symposium, Corsica, France, 2009.

Stern-Gottfried, J., Rein, G., and Torero, J.L., "An Experimental Review of the

Homogeneous Temperature Assumption in Post-Flashover Compartment

Fires”. International Congress on Fire Protection and Life Safety in Buildings and

Transportation Systems, Santander, Spain, 2009.

Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel guide”, Fire Risk

Management, November 2009, pp. 12-16.

Stern-Gottfried, J., Rein, G., and Torero, J.L., "A Performance Based

Methodology Using Travelling Fires for Structural Analysis". 8th International

Conference on Performance-Based Codes and Fire Safety Design Methods, Lund

University, Sweden, June 2010.

Stern-Gottfried, J., Rein, G., and Torero, J.L., "Experimental Review of the

Homogeneous Temperature Assumption in Post-Flashover Compartment

Fires”. The 12th International Interflam Conference, University of Nottingham, UK,

July 2010.

Jonsdottir, A., Rein, G., and Stern-Gottfried, J., “Comparison of Resultant Steel

Temperatures Using Travelling Fires and Traditional Methods: A Case Study of

the Informatics Forum Building”. The 12th International Interflam Conference,

University of Nottingham, UK, July 2010.

Rein, G. and Stern-Gottfried, J., “Travelling Fires in Large Compartments:

Realistic fire dynamics for structural design”, International Conference on

Applications of Structural Fire Engineering, Prague, Czech Republic, Prague,

Czech Republic, 2011.

Page 17: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xv

Posters

Stern-Gottfried, J., Rein, G., Lane B., and Torero, J.L., "Design Fires for

Structural Analysis of Complex Buildings". The 9th International Symposium on

Fire Safety Science, Karlsruhe, Germany, 2008.

Stern-Gottfried, J., Rein, G., and Torero, J.L., "Experimental Review of the

Homogeneous Temperature Assumption in Post-Flashover Compartment

Fires". Spring Meeting of the British Section of the Combustion Institute, Edinburgh,

UK, 2010. (Awarded Best Poster).

Awards

David B. Gratz Scholarhip, 2010. Awarded by the Fire Safety Educational

Memorial Fund of the National Fire Protection Association (NFPA) in the USA

to a graduate student in Fire Science located outside the USA and Canada who

demonstrates scholarship achievement, leadership qualities, concern for

others/volunteerism, and contributions to international/national fire safety

activities.

Page 18: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xvi

Page 19: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xvii

Preface

This thesis is written in manuscript format. As such each chapter is a standalone

document suitable for journal publication. The material is presented as follows:

Chapter 1 is a brief introduction to the concept of travelling fires and the

research presented in this thesis. While not a full manuscript, it is loosely based

on:

Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel Guide”, Fire Risk

Management, November 2009. pp. 12-16.

Chapter 2 presents a review of the homogeneous temperature assumption in

post-flashover fires that is invoked in many compartment fire models. This

manuscript has been published as:

Stern-Gottfried, J., Rein, G., Bisby, L.A., and Torero, J.L., “Experimental

review of the homogeneous temperature assumption in post-flashover

compartment fires”. Fire Safety Journal, Vol. 45, 2010, pp. 249-261.

Chapter 3 is a literature review of research in travelling fires for structural

analysis. This manuscript has been submitted for journal publication.

Chapter 4 presents a collaborative research effort with structural fire engineers.

The chapter investigates the impact of the travelling fires methodology

Page 20: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

xviii

developed in this thesis on a generic concrete frame. In this work, I quantified

and reported on the thermal environment. The lead author performed and

reported on the structural analysis as part of his PhD thesis. This manuscript

has been published as:

Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of

travelling fires on a concrete frame”, Engineering Structures, Vol. 33, 2011,

pp. 1635-1642.

Chapter 5 presents the detailed development of the travelling fires

methodology with application to heating of a generic concrete structure. This

manuscript has been submitted for journal publication.

Chapter 6 is a conclusion for this thesis and presents recommended future

work. This chapter is not intended to be a published manuscript.

Appendix A provides details of the heat transfer calculations utilised in

Chapters 2 and 5.

Page 21: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

1

1 Introduction

Close inspection of accidental fires in large, open-plan compartments reveals that

they do not burn simultaneously throughout the entire enclosure. Instead, these

fires tend to move across floor plates as flames spread, burning over a limited area

at any one time. These fires have been labelled “travelling fires”.

Despite these observations, fire scenarios currently used for the structural fire

design of modern buildings are based on traditional methods that come from the

extrapolation of existing fire test data. Most of these data stem from tests performed

in small compartments that are almost cubic in nature. This test geometry allows for

good mixing of the fire gases and thus for a relatively uniform temperature

distribution throughout the compartment. While this behaviour is different from

that observed in real fires, it has generally been deemed a conservative, and

therefore appropriate, approach for structural fire design in the absence of better

and more relevant data. This approach might be considered acceptable for most

Page 22: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

2

design cases, but the need for better optimisation of structural behaviour in fire will

eventually require a more realistic definition of the fire.

Computational methods for determining structural behaviour have matured over

the last decade and have enabled analysis of more complex structural systems. This

has led to an understanding that many modern structures do not behave in the same

manner as simpler, more traditional frame based systems. In order to address these

differences, and continue to enable innovation in structural design, a more

sophisticated characterisation of fire scenarios is required.

This thesis reviews the assumptions inherent in the traditional methods and

addresses their limitations by proposing a methodology to consider travelling fires

for structural design. Central to this work is the need for strong collaboration

between fire safety engineers to define the fire environment and structural fire

engineers to assess the subsequent structural behaviour.

1.1 Traditional Methods

It is important to understand the context of the current design methods to establish

a new methodology for design fires for structural analysis. Traditionally, structural

fire analysis has been based on one of two methods for characterising the fire

environment:

• The standard temperature-time curve (as specified by various standards,

such as BS 476 [1], ISO 834 [2], and ASTM E119 [3])

• Parametric temperature-time curves (such as that specified in Eurocode 1

[4]).

While both of these methods have great merits and represented breakthroughs in

the discipline at their times of adoption, it is recognised that they have limitations.

Page 23: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

3

The standard temperature-time curve, which is used as the basis for the fire rating

system in most building codes and standards worldwide, was first published in

1917 [5]. The curve came from collating various fire tests into one idealised curve.

The tests that fed into the development of the standard fire were intended to

represent worst case fires in enclosures so that the structure could withstand

burnout. However, these tests were conducted and the standard fire created prior to

much scientific understanding of fire dynamics. Thus the standard fire, unlike a real

fire, has a relatively slow growth period, never reduces in temperature due to fire

decay, and is independent of building characteristics such as geometry, ventilation

and fuel load.

The next major landmark for structural fire analysis, in terms of design, was a

guidance document produced in Sweden in 1976 [6]. This work incorporated the

current understanding of compartment fire dynamics based on tests conducted in

small scale enclosures. The document presented the key factors of compartment fire

temperatures as the fuel load, ventilation, and the thermal properties of the wall

linings. The guide gave design recommendations and a series of temperature-time

curves for a wide range of the critical parameters, accounting for the cooling period

of the fire.

The Eurocode parametric temperature-time curve is based on the same fire science

as the Swedish design guide. The Eurocode parametric temperature-time curve was

developed to collapse all of the curves given in the Swedish guidance document

into a simplified mathematical form.

Eurocode 1 [4] states that the design equations for the parametric temperature-time

curve specified are only valid for compartments with floor areas up to 500m2 and

heights up to 4m. In addition the enclosure must have no openings through the

ceiling and the thermal properties of the compartment linings must be within a

limited range. As a result, common features in modern construction like large

Page 24: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

4

enclosures, high ceilings, atria, large open spaces, multiple floors connected by

voids, and glass façades are excluded from its range of applicability. These

limitations, which are largely associated with the physical size and geometric

features of the experimental compartments on which the methods are based, ought

to be carefully considered when the method is applied to an engineering design

beyond the recommended ranges of applicability. This is particularly relevant given

the large floor plates and complicated architecture of modern buildings.

It is noted that the background document to the UK National Annex of Eurocode 1

[7] suggests that designers can ignore the given limitations on floor area and

compartment height and can expand the range of the compartment lining values.

While this allows engineers to use the equations on more practical applications, it

does not appear to address the observed travelling nature of real fires in large

compartments.

1.2 Non-Uniform Burning

The traditional methods mentioned above for specifying design fires for structural

engineering analysis assume spatially homogeneous temperature conditions. The

accuracy and range of validity of this assumption is examined in Chapter 2, using

the previously conducted fire tests of Cardington (1999) and Dalmarnock (2006).

Statistical analyses of the test measurements provide insights into the temperature

fields in the compartments. The temperature distributions are statistically examined

in terms of dispersion from the spatial compartment average. The results clearly

show that uniform temperature conditions are not present and variations from the

compartment averages exist. Peak local temperatures range from 23% to 75% higher

than the compartment average, with a mean peak increase of 38%. Local minimum

temperatures range from 29% to 88% below the spatial average, with a mean local

minimum temperature of 49%. The experimental data are then applied to typical

structural elements as a case study to examine the potential impact of the gas

Page 25: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

5

temperature dispersion above the compartment average on element heating.

Compared to calculations using the compartment average, this analysis results in

increased element temperature rises of up to 25% and reductions of the time to

attain a pre-defined critical temperature of up to 31% for the 80th percentile

temperature increase. The results show that the homogeneous temperature

assumption does not hold well in post-flashover compartment fires. Instead, a

rational statistical approach to fire behaviour could be used in fire safety and

structural engineering applications.

This heterogeneity of the temperature field will be more pronounced when the

burning itself is not uniform, as is the case in travelling fires. A travelling fire is

when only a portion of a floor plate is fully involved in flames that then move to

other areas of the floor as burnout occurs in locations of earlier burning. The fire

travels as flames spread to unburnt fuel, partitions or false ceilings break and

ventilation changes through glazing failure.

Many large, accidental fires, such as those in the World Trade Center Towers 1, 2 [8]

and 7 [9] in New York in 2001, the Windsor Tower in Madrid, Spain in 2005 [10] and

the Faculty of Architecture building at TU Delft in the Netherlands in 2008 [11] were

all observed to travel across floor plates, and vertically between floors, rather than

burn uniformly for their duration. Similar observations were made of the Interstate

Bank fire in Los Angeles in 1988 [12] and the One Meridian Plaza fire in

Philadelphia in 1991 [13]. Travelling fires have also been observed experimentally in

compartments with non-uniform ventilation [14, 15, 16].

1.3 Travelling Fires

Based on the above, it can be seen that the concept of travelling fires is in direct

contrast to the fundamental nature of current design methods that assume uniform

conditions throughout a compartment for the entire duration of burning of a fire.

Page 26: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

6

A fire that burns uniformly within a large enclosure would generate high

temperatures, but only for a relatively short duration. However, a fire that travels

will still create elevated temperatures away from the fire (the far field) as well as

flame temperatures in the near field. A travelling fire can therefore inflict the

structure with elevated temperatures for longer durations. A travelling fire is

illustrated in Figure 1.1, showing the difference between the near field and far field.

Figure 1.1: Illustration of a travelling fire.

Due to the discrepancy between fire behaviour in actual incidents and that assumed

in traditional design methods, it is possible that current practices for structural

design do not consider a potentially worst case fire scenario. Non-uniform heating

across a compartment floor could cause a failure mechanism in the structure which

may not occur if uniform temperatures were applied to the structure. For example, a

cool, unheated bay in a multi-bay structure could produce high axial restraint forces

and that could result in failure of a heated element. In other situations, however,

traditional design methods may be overly conservative compared to the impact of a

real fire.

Far field (Tff) Near field (Tnf)

Near field

travels over

time

Page 27: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

7

1.4 A New Methodology

To address the limitations of the traditional methods, and provide the necessary

tools to enable a more realistic determination of a building’s response to fire, a

methodology has been developed that can incorporate the actual dynamics of a

travelling fire into structural analysis. This methodology will better enable

structural and architectural design innovation.

Chapter 3 is a literature review of travelling fire research. A brief background to the

traditional methods that assume uniform fires is given along with critiques of that

assumption, such as the heterogeneity of compartment temperatures and the

observation of travelling fires in both accidental events and controlled tests. The

research in travelling fires is reviewed, highlighting the pioneering work in the field

to date. The main challenge in developing tools for incorporating travelling fires

into design is the lack of large scale test data. Nonetheless, significant progress in

the field has been made and a robust methodology using travelling fires to

characterise the thermal environment for structural analysis has been developed.

The research in quantifying the structural response to travelling fires is also

reviewed.

Chapter 4 presents a collaborative analysis between fire engineers and structural fire

engineers. A basic version of the travelling fires methodology, using a family of

fires, is applied to a framed concrete structure. A Finite Element Model of the

generic concrete structure is used to study the impact of the family of fires; both

relative to one another and in comparison to the conventional methods. It is found

that travelling fires have a significant impact on the performance of the structure

and that the current design approaches cannot be assumed to be conservative.

Further, it is found that a travelling fire of approximately 25% of the floor plate in

size is the most severe in terms of structural response. It is concluded that the

Page 28: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

8

travelling fires methodology is simple to implement, provides more realistic fire

scenarios, and is more conservative than current design methods.

Chapter 5 gives a more developed version of the methodology. Many of the

assumptions of the method are explored, and a robust spatial discretisation scheme

is adopted to characterise the far field variation of a linearly travelling fire. Heating

of a similar concrete structure to that used in Chapter 4 is examined. A detailed

sensitivity study is also conducted, highlighting the critical parameters for design. It

is found that the most sensitive parameters are related to the building design and its

use and not the physical assumptions or numerical implementation of the model.

1.5 Collaboration

As the disciplines of fire science and structural engineering are very disparate in

their knowledge base, but have a strong overlap in their application to structural

fire analysis, a high degree of collaboration between these disciplines is required

[17]. The travelling fires methodology developed and presented in this thesis has

been formulated with precisely this degree of multidisciplinary cooperation in

mind.

References

1 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:

Method for Determination of the Fire Resistance of Elements of Construction:

BSI, 1987.

2 ISO 834-1. Fire-resistance tests — Elements of building construction — Part 1:

General requirements

3 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings

Construction and Materials, 2000.

Page 29: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

9

4 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on

structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.

5 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance

testing – Part II.” Fire Technology, Vol. 14, 1978, pp. 304-316.

6 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel

Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,

1976.

7 PD 6688-1-2:2007 Background paper to the UK National Annex to BS EN 1991-

1-2

8 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,

Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the

World Trade Center Towers. NIST NCSTAR 1-5, 2005.

9 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,

Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire

Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST

NCSTAR 1-9, 2008.

10 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based

analysis of a concrete building subjected to fire,” Advanced Research Workshop on

Fire Computer Modelling, Santander, Spain, 2007,

http://www.era.lib.ed.ac.uk/handle/1842/1988.

11 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT

Instituut voor Veilingheids – en Crisismanagement, 2008.

12 Routley, J.G., “Interstate Bank Building Fire, Los Angeles, California”, U.S. Fire

Administration Technical Report 022.

13 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One

Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration

Technical Report 049.

Page 30: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

10

14 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation

Openings – Comparison of Long and Wide Enclosures”, The 6th International

Symposium on Fire Safety Science, Poitiers, France, 1999.

15 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,

“Natural Fires in Large Scale Compartments”, British Steel, 1994.

16 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of

the homogeneous temperature assumption in post-flashover compartment

fires”. Fire Safety Journal, 45, 2010, pp. 249-261.

17 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires.”

The 9th International Symposium on Fire Safety Science, Karlsruhe, Germany, 2008.

Page 31: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

11

2 Experimental Review of

the Homogeneous Temperature

Assumption in Post-Flashover

Compartment Fires

2.1 Introduction

Post-flashover compartment fires are of particular relevance to the analysis of

structural fire performance because of their high severity. Traditional methods for

quantifying and modelling post-flashover fires for structural engineering analysis

assume homogeneous temperature conditions, i.e. the gas phase temperature

distribution is taken to be spatially uniform and does not have considerable

gradients. For example, the methodologies for structural fire analysis that use the

standard and parametric temperature-time curves assume this uniform temperature

Page 32: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

12

regardless of the compartment size or fire power. This assumption has been

necessary to develop simple analytical solutions to the temperature evolution and

further the understanding of post-flashover compartment fires and subsequent

structural responses [1].

However, the accuracy and range of validity of the homogeneous temperature

assumption has not been thoroughly examined before. This is generally due to the

limited number of post-flashover fire experiments available and especially to the

low spatial resolution of temperature measurements used in such tests.

This paper reviews the validity of this assumption using previously conducted fire

tests. The tests chosen for these analyses are the Cardington (1999) and Dalmarnock

(2006) tests. The choices are based on the detailed instrumentation and the large

geometry of the tests. The paper also examines the impact of the departure from the

homogeneous temperature assumption on typical thermal analyses that represent

the basis behind structural fire calculations.

2.2 The Homogeneous Temperature Assumption

2.2.1 Origins of the Assumption

Most theoretical models for quantifying the temperature evolution in post-flashover

fires are based on the assumption of uniform compartment temperatures [2], which

is also referred to as the well stirred reactor assumption. This is the case for both

analytical models and zone models. Karlsson and Quintiere [1] note that this

assumption, among others, is required for an analytical solution of the energy

balance for the compartment. In particular they note that the methods of

Magnusson and Thelandersson in 1970 [3] and Babrauskas and Williamson in 1978

[4] adopted this approach. The former is the basis for the Eurocode parametric

temperature time curve [1]. Drysdale [5] notes that a justification of this assumption

often used is that there is supposedly a small gradient in the vertical temperature

Page 33: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

13

distribution during a post-flashover fire and even smaller horizontal gradients. For

example, a single test from 1975 is cited showing a nearly uniform vertical

temperature distribution at one moment at the onset of flashover [5]. However, this

justification has not been evaluated any further. Furthermore, due to the limited

number of thermocouple trees in most fire tests (typically one or two), the presence

of horizontal gradients cannot be investigated and is rarely reported.

Franssen proposed modifications to the Eurocode parametric temperature-time

curve to better correlate the predicted peak temperatures with those from 48

experiments [6]. However, dispersions of the temperature data about the

compartment averages for the experiments are not given, presumably because the

assumption of temperature uniformity was automatically invoked.

The uniform temperature assumption is fundamentally inherent in the test methods

used for classifying structural fire resistance. The fire rating system adopted by most

building codes and standards worldwide is based on single elements of construction

being subjected to furnace tests in which the gas temperature evolution follows that

of a uniform standard fire. It is a key aim of these tests to produce as uniform a

temperature field as possible throughout the furnace. Typical furnace tests include

about four to nine thermocouple or plate thermometer measurements in different

locations. ISO 834 [7] specifies the compartment temperature as the spatial average

from all of the thermocouples monitoring the gas phase. The test requires that each

individual thermocouple be within 100°C of the standard fire temperature-time

curve specified at all times after the initial 10min. The test also requires that the

percentage difference between the areas under the measured compartment average

and the standard temperature-time curves be within 15% of each other after the first

10min, 10% after 30min, 5% after 60min, and 2.5% thereafter. BS 476 [8] and ASTM

E119 [9] have similar tolerances.

Page 34: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

14

The tight tolerances required in standard fire tests are specifically set to ensure that

the temperature field in the compartment is uniform. While standard fire curves

have been criticised before on many counts for not representing natural fires [5, 6,

10], the spatially homogeneous temperature assumption has not typically been one

of them.

2.2.2 Critiques of the Assumption

Harmathy [11] presents a qualitative critique of the homogeneous temperature

assumption, also referred to as the well stirred reactor assumption. The critique

states that external flaming close to a vent invalidates the well stirred reactor model.

Harmathy suggests division of the compartment into three zones to allow

mathematical treatment: a zone of primarily fresh incoming air, a zone dominated

by the presence of the flame, and a zone behind the flame with mixed pyrolyzates

and combustion products. According to this classification, the homogeneous

temperature distribution would only be valid in this last zone. However, this

critique does not provide any quantification of the heterogeneity or its effects.

Bøhm and Hadvig [12] reported differences in experimental temperature

measurements of 200 to 500°C within a single post-flashover fire, with the hottest

temperatures in the centre of the compartment. Their test compartment was 4.6m x

4.6m x 2.5m, and temperature measurements were made at eight different locations.

The temperature differences led to difficulties in predicting the heat fluxes to both

the fuel surface and the exposed structure, but no further analysis was made of the

effect of the non-uniformity.

Welch et al. [13] and Abecassis et al. [14] reviewed the experimental data of the

Cardington Tests and the Dalmarnock Fire Tests, respectively, in terms of

temperature and heat flux fields and concluded they did not support the

conventional assumption of uniformity. These tests are described in Section 2.3.3.

Page 35: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

15

2.3 Experimental Review

The presence of considerable temperature gradients during post-flashover fires has

previously been observed, although not systematically examined. Tests in large or

irregularly shaped compartments and real fires can provide insight into the

potential dispersion of temperatures and are reviewed here.

2.3.1 Non-Uniform Burning in Experiments

Kirby et al. [15] ran a test series burning wood cribs in a long enclosure with

approximate dimensions of 22.9m long x 5.6m wide x 2.8m high. All of the tests

were ignited at the rear, except one in which all wood cribs were ignited

simultaneously. The results of all tests show that the fire moved relatively quickly

from the ignition location to the front of the compartment, where the vent was

located. After the fuel in the front of the compartment burnt out, the fire

progressively travelled back into the compartment and ultimately consumed all the

fuel and self-extinguished at the rear. Temperature results of Test 1 from this test

series are shown below in Figure 2.1 at the rear, middle and front of the

compartment.

Thomas and Bennetts [16] conducted a test series of ethanol pool fires in a small

rectangular enclosure (1.5m x 0.6m x 0.6m) to determine the influences of ventilation

size and location on the burning rate. They found that there were significant

differences in burning rates between having the opening on the short end (long

enclosure) or the long side (wide enclosure). They observed temperature differences

at different locations up to 500°C, generally with greater temperatures nearer the

vents, as this is where the flames resided more often. This work was continued

further [17] with another experimental series of pool fires in a larger, long enclosure

(8m x 2m x 0.6m), in which the opening size on the short end was varied. The results

obtained were similar to both their earlier work [16] and that of Kirby et al. [15].

Page 36: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

16

They conclude that a structural element near the vent would be exposed to more

severe conditions than one further inside the compartment.

Figure 2.1: Comparison of temperature-time measurements at three different locations,

spaced 8m apart, from the rear to the front of the compartment, illustrating non-

uniform burning during of wood cribs during the tests of Kirby et al. [15].

2.3.2 Travelling Fires

Since the scale of most enclosures in real buildings is significantly larger than the

scale in the few experimental tests available, it is likely that even higher degrees of

non-uniformity are to be expected in real fires. The real, large fires in the World

Trade Center towers 1, 2 [18] and 7 [19] in New York in September 2001, the

Windsor Tower in Madrid, Spain in February 2005 [20] and the Faculty of

Architecture at TU Delft in the Netherlands in May 2008 [21] were all observed to

travel across floor plates. Due to the travelling nature of the fires, it is likely that

temperature distributions during these events were highly non-uniform. While no

data exist to validate this, extensive numerical simulations conducted for the World

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Tem

pe

ratu

re (°

C)

Time (min)

Rear

Middle

Front

Page 37: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

17

Trade Center investigations by NIST clearly show temperature variations within

single compartments of several hundred degrees Celsius [18, 19].

2.3.3 Fire Tests with High Spatial Resolution

Traditionally, most fire tests have only limited spatial resolution in temperature

measurements. For example, the series of well ventilated fire tests conducted by

Steckler et al. [22], which are often cited in fire model validation studies, monitored

the vertical distribution of gas temperatures at only two locations; at the vent and at

one internal corner of the compartment. This low spatial resolution cannot provide

the necessary insight into the degree of temperature homogeneity and leaves the

uniformity assumption unchallenged.

More recent tests, such as the Dalmarnock Fire Tests [23, 14] in 2006 and the Natural

Fire Safety Concept 2 test series at Cardington [24, 13] in 1999, have included a

much greater spatial resolution of instrumentation. General overviews of these

experimental setups are provided here.

The Dalmarnock Fire Tests, which provide the greatest instrumentation density to

date, were conducted in a real high-rise apartment building in Glasgow, UK [23, 14].

The two tests conducted had a realistic fuel load of typical residential/office

furnishings. The compartment was 4.75m x 3.50m x 2.45m, containing 20

thermocouple trees, each with 12 thermocouples (placed 0, 0.05, 0.1, 0.2, 0.3, 0.4, 0.6,

0.8, 1.0, 1.3, 1.6 and 2m from the ceiling). The Dalmarnock experimental layout is

given in Figure 2.2. Ignition occurred in the waste-paper basket adjacent to the sofa.

Two tests were conducted, however only Test One is examined as the fire in the

second test was manually suppressed before flashover.

Page 38: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

18

Figure 2.2: Experimental layout of the Dalmarnock Test One [23, 14]. Locations of the 20

thermocouple trees (each with 12 thermocouples in height) are noted by blue

crosses.

The eight Cardington Tests were conducted in a room 12m x 12m x 3m with

uniformly spaced fuel load packages distributed across the floor [24, 13]. Sixteen

thermocouple trees containing four thermocouples each were placed on a uniform

grid in the compartment to record the gas temperatures, shown in Figure 2.3. The

tests were conducted with various combinations of fuel type, ventilation

distribution, and interior lining material. The tests had liquid fuel channels

connecting the fuel packages so that ignition and the subsequent burning could be

as uniform as possible.

4.75m

3.5m

Page 39: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

19

Figure 2.3: Experimental layout of Cardington Tests [24, 13]. Locations of the 16

thermocouple trees (each with 4 thermocouples in height) are noted by black

dots.

The Cardington experiments intended to test two types of compartment insulation;

“insulating” (I) and “highly insulating” (HI). However, after Test 1 the “highly

insulating” material was placed on the ceiling for all remaining tests, creating an

intermediate level of insulation (I+). The fuel packages were either just wood cribs

(W) or a combination of wood and plastic cribs (W+P). The ventilation openings

were either fully open on the front (F) of the enclosure or on the front and back

(F+B). A summary of these parameters for all eight tests is given in Table 2.1.

Test Number 1 2 3 4 5 6 7 8

Fuel Type W W W+P W W+P W W+P W+P

Insulation Type I HI HI HI HI I+ I+ I+

Opening Location F F F F+B F+B F+B F+B F

Table 2.1: Summary of test conditions in Cardington [24, 13].

Both data sets have a sufficient number of data points to allow for representative

statistical analyses. Dalmarnock had 240 points and the Cardington Tests each had

64. The Dalmarnock tests have both well distributed measurement points and a high

12m

12m

Page 40: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

20

density of instrumentation (5.9 thermocouples/m3). The Cardington Tests had well

distributed measurement points, but not a high density of instrumentation

(0.15 thermocouples/m3).

The Dalmarnock test data were corrected for thermocouple radiation errors using

the method of Welch et al. [13]. The Cardington data have not been corrected.

However, Welch et al. [13], using Cardington Test data, report that typically

corrections fall in the range of 10 – 40°C, with occasional values as high as 100°C for

flame temperatures. Additional calculations were performed using the

thermocouple corrections for one of the Cardington Tests to confirm that similar

results were obtained to those presented in this study.

The results from Dalmarnock Test One are given in Figure 2.4. The results are

shown with the average compartment temperature and standard deviation in the

shaded region, plus the maximum and minimum temperature measurements in the

compartment at any given time. Two distinct post-flashover periods can be

observed in the Dalmarnock data. The change between the first and second period is

caused by window breakage at approximately 13.5 minutes after ignition. The

spatial location of the hot and cold spots can be investigated tracking the maximum

and minimum temperature curves. Through the test, the maximum temperature

was registered at different times in 52 thermocouple locations, distributed over 16

out of the 20 thermocouple trees and all but one of the 12 heights. No particular

pattern of where the peak temperatures were located is observed. The minimum

temperature was registered at only three different thermocouple locations

(thermocouple trees 4, 6, and 18 shown in Figure 2.2) all at the lowest thermocouple

(0.45m above the floor). All three locations are near pathways for make-up air to the

fire compartment.

Page 41: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

21

Figure 2.4: Experimental results of Dalmarnock Test One [23, 14] showing the

compartment average, maximum and minimum temperatures, and the

standard deviation. Flashover occurred at 5min, window breakage at 13.5min,

and the fully developed fire lasted until suppression at 19min.

The results for all eight of the Cardington Tests are shown in Figure 2.5. Note that

there was a period between 16 and 22 min of Cardington Test 1 where data

collection was temporally lost (interpolation is provided).

The general results are summarised in Table 2.2 which provides the minimum,

mean, and maximum standard deviations, as well as the maximum average

compartment temperature reached for each test. The standard deviations are only

included for portions of the tests where the average compartment temperatures are

above 500°C, as the interest of this examination lay in the post-flashover portion of

the experiments. Table 2.2 also presents averaged values for two different furnace

tests conducted on the same wall assembly to the ASTM E119 standard fire in April

2009 [25]. The tests, carried out at a commercial laboratory to provide a rating for a

bespoke wall assembly, included nine gas phase thermocouples.

0

200

400

600

800

1000

0 5 10 15 20

Tem

pe

ratu

re (°

C)

Time (min)

Avg

ssss

Max

Min5 min

13.5 min

19 min

Page 42: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

22

Figure 2.5: Experimental results of the Cardington Tests [24, 13] showing compartment

average, maximum and minimum temperatures, and the standard deviation for

each test. See Table 2.1 for a summary of conditions for each test.

Cardington 1

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 2

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 3

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 4

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 5

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 6

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 7

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Cardington 8

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time (min)

Temperature (°C

)

Page 43: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

23

Test Min � (°C)

Mean � (°C)

Max � (°C)

Max ���� (°C)

Dalmarnock Test One 105 132 233 733

Cardington 1 38 84 136 857

Cardington 2 31 83 153 1075

Cardington 3 31 100 208 1103

Cardington 4 31 52 93 1199

Cardington 5 18 56 135 1147

Cardington 6 25 44 129 1218

Cardington 7 20 51 159 1200

Cardington 8 32 83 213 1107

Standard Fire Tests 8 12 39 N/A

Table 2.2: Summary of the temperature measurements of each spatially resolved fire test

and the mean values of two standard fire tests to ASTM E119.

In addition to the values shown in the Table 2.2, peak local temperatures range from

23% (Cardington Test 6) to 75% (Dalmarnock Test One) higher than the

compartment average, with a mean peak increase of 38% across all tests. Local

minimum temperatures range from 29% (Cardington Test 4) to 88% (Dalmarnock

Test One) below the compartment average, with a mean local minimum

temperature of 49% across all tests.

Higher mean standard deviations are observed in Dalmarnock Test One (132°C)

than all of the Cardington Tests (mean of 70°C). This is to be expected for several

reasons:

• Dalmarnock Test One had a much higher density of instrumentation than

the Cardington Tests, making it more likely that the full range of

temperature conditions was recorded.

• The thermocouple layout in Dalmarnock Test One covered regions with fuel

packages and regions remote from fuel packages. In Cardington, all

thermocouples were located above fuel packages and thus the data have a

bias towards flame temperatures.

Page 44: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

24

• There were only four different thermocouple heights in the spacing of the

Cardington Tests, all relatively high, compared to the twelve in Dalmarnock,

which were evenly distributed. Thus the Cardington data are biased towards

temperatures in the upper portion of the compartment.

• The Dalmarnock Test had a realistic fire scenario where real-world

furnishings were arranged in a non-uniform manner and one ignition point

was used. In contrast, the Cardington Tests had well distributed fuel

packages ignited simultaneously.

A clear trend can be seen in the results from Cardington. Tests 4 through 7 all have

lower standard deviations (mean of 51°C) than Tests 1, 2, 3, and 8 (mean of 88°C).

The key difference between the two groups of tests is the ventilation position. Tests

1, 2, 3, and 8 had ventilation only on one side of the compartment, while Tests 4

through 7 had ventilation at two opposing sides. This fact is in line with the results

obtained by the studies previously highlighted with long enclosures [15, 16, 17].

Thus there is heterogeneity in the temperature field due to the depth of the

compartment relative to the position of the vents. This effect is less obvious for the

tests with ventilation on opposing sides.

These results confirm that there is considerable heterogeneity in the temperature

field of post-flashover fires. Real world fires are likely to have a level of dispersion

in the temperature field closer to that measured in Dalmarnock Test One than those

of the Cardington Tests. This is because the high density of instrumentation in

Dalmarnock recorded more of the temperature field than those in the Cardington

Tests, thus a more complete depiction of the variation was established. Furthermore,

the fuel types and distributions of real world fires that can cause heterogeneity are

more likely to match those of Dalmarnock than the uniformly spaced cribs of

Cardington.

Page 45: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

25

It is also worth noting that the tests examined were conducted in compartments of

dimensions that are consistent with the homogeneous temperature assumption.

Thus other compartments with larger or more complex geometries will show

broader temperature dispersions.

2.3.4 Data Distributions

Examination of the statistical distributions of the data from each test provides more

insight into the level of uniformity of the temperature field. Figure 2.6 presents the

data distributions for four different times of Dalmarnock Test One with the

corresponding normal distribution overlaid. The distributions are shown at four

times, evenly spaced between flashover and suppression. The temperature

measurements are grouped into 40°C bands, as to encompass the experimental

uncertainty. If the homogeneous temperature assumption held, there would only be

one bar at any given time.

Figure 2.6: Comparisons of the measured temperature distributions against the associated

normal distributions after flashover for Dalmarnock Test One.

5 min after Flashover (10 min)

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200

Temperature (°C)

Probability

1 min after Flashover (6 min)

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200

Temperature (°C)

Probability

Data

Normal Distribution

13 min after Flashover (18 min)

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200

Temperature (°C)

Probability

9 min after Flashover (14 min)

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200

Temperature (°C)

Probability

Page 46: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

26

Figure 2.7 and Figure 2.8 provide details for the data distributions of the Cardington

Tests. Figure 2.7 presents the data distributions for the four Cardington Tests with

ventilation at one side only (F), while Figure 2.8 presents the data distributions with

ventilation on opposing sides (F+B). The F data show a greater span in the

distributions than the F+B data.

The test data have been presented with standard deviations as a measure of the

departure from uniform temperature conditions. For a simplified estimation of the

meaning of the standard deviation, it is noted that approximately 65% of all data fall

within the span between one standard deviation on either side of the average and

approximately 95% fall within the same span of two standard deviations.

While the data distributions shown in Figures 2.6 through 2.8 do not always fit

normal distributions, at most times for most tests they are sufficiently close to treat

the data as normally distributed for the purposes of this analysis.

2.3.5 Standard Deviation vs. Temperature Rise

Figure 2.9 shows the relationship between the normalised standard deviation, σ�, and the average temperature rise from ambient, ∆�� . Each data point represents

one instant in time, with one point taken every minute for each test. The normalised

standard deviation, ��, is defined as the standard deviation divided by the average

compartment temperature rise above ambient, ∆�� . The Cardington Tests have

been divided into the two ventilation groups previously noted. Cardington F is the

group with ventilation in the front only and Cardington F+B is the group with

ventilation from both the front and back.

Page 47: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

27

Figure 2.7: Comparisons of the measured temperature distributions against the associated

normal distributions for Cardington Tests with ventilation on one side only

(Tests 1, 2, 3 and 8).

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 8

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 3

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 2

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 1

Page 48: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

28

Figure 2.8: Comparisons of the measured temperature distributions against the associated

normal distributions for Cardington Tests with ventilation on opposing sides

(Tests 4, 5, 6 and 7).

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 7

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 6

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 5

50 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

30 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

10 min

0

0.1

0.2

0.3

0.4

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Probability

Cardington 4

Page 49: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

29

Figure 2.9: Observed relationship between the normalised standard deviation vs.

temperature rise in the spatially resolved fire tests available.

These results indicate that there are significant heterogeneities in the gas field across

the whole range of temperatures. Furthermore, the scatter shows a clear trend; the

higher the temperature, the lower the normalised standard deviation. The

maximum temperature rise, just above 1200°C, marks the peak flame temperature

rise above ambient, which is at the upper end of temperature rises possible in a

typical post-flashover fire. More intense fires lead to hotter and more uniform

conditions in their enclosures, whereas in less intense fires the flame and smoke

regions dominate less of the gas field and less uniformity is observed. A clear

difference can be seen in the ventilation effect between the two groups from the

Cardington Tests, with the Cardington F Tests having less homogeneity than

Cardington F+B Tests. Also the greater degree of heterogeneity from the

Dalmarnock test can be seen.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 200 400 600 800 1000 1200

σ' (°C

/°C

)

ΔTavg (°C)

Dalmarnock

Cardington F

Cardington F+B

Middle of Envelope

Page 50: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

30

The shaded region represents an approximate envelope for all of the data points.

The best fit equation for the curve that runs through the middle of this envelope is

given in Eq. (2.1).

�� = �∆�� = 1.939 − 0.266���∆�� � (2.1)

This curve could be used as a nominal expression of the standard deviation for any

temperature-time curve. The shaded envelope could be expected to apply to fires in

compartments of similar sizes as those assessed in this paper. For fires in

compartments of a much larger size, such as the real ones previously cited [18, 19,

20, 21], the temperature field will likely be much more non-uniform and a travelling

fire should be expected. A general discussion of the temperature fields in travelling

fires is available in the literature [26, 27].

The middle of the envelope has been used in lieu of a regression analysis because

the data are biased towards the Cardington Tests due to the large number of data

points for each test. There were eight Cardington Tests and each lasted longer than

Dalmarnock Test One. Therefore the shaded envelope was used to eliminate any

bias towards the Cardington data. For the reasons already discussed, the

Cardington data are deemed inappropriate to express standard deviations for a

general, real fire scenario.

2.4 Effect of Temperature Heterogeneity on the

Structure

Structural fire resistance calculations are routinely based on averaged temperature

values determined on the basis of standard fire tests conducted in test furnaces

which are explicitly intended to ensure uniform gas phase temperatures. However,

recent studies have shown that the behaviour of certain structural elements are

Page 51: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

31

affected by temperature gradients [28, 29], thus there is a motivation to revisit the

homogeneous temperature assumption. Moreover, the experimental results

analysed above are at odds with the traditional assumption of temperature

uniformity, thus the effect of this heterogeneity on the heating of structural elements

is reviewed here.

A simplistic method for assessing the impact of non-uniform temperature

distributions on single structural elements has been adopted. These calculations are

intended to provide insight into the performance of simple structures and are not

proposed to be a design methodology or calculation guideline. Further research is

required to determine true structural response to non-uniform heating as the

analysis of the fire test data indicates that the use of a uniform temperature

distribution does not capture the true thermal environment of a real fire. Therefore

these simplistic calculations have only been adopted for illustrative purposes, to

examine trends for structures heated to temperatures above the compartment

average.

It is important to clarify that the impact of non-uniform temperature distributions

on full structural behaviour is not being assessed here, nor issues associated with

details of heat transfer such as soot concentrations or velocities. While these details

will have an impact on the heating of structural elements, they are not usually part

of standard thermal calculations for the purposes of structural fire analysis.

For illustrative purposes, three simplified examples of structural elements are used:

(1) an unprotected steel I-beam, (2) a protected steel I-beam fire rated to 60 min

using a generic insulation, and (3) a concrete beam with a 60 min fire rating. All

three beams, with dimensions given in Figure 2.10, nominally have the same design

bending moment capacity under ambient temperature. The beams selected for the

analysis are representative of typical beams covering the most common construction

types and range of thermal inertias found in real buildings. The unprotected and

Page 52: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

32

protected steel beams have the same dimensions, except that an additional layer of

fire protection is applied to the protected beam (12 mm of high density perlite

insulation). It is assumed that a concrete floor slab is present above the beams such

that they are only heated on three sides.

Figure 2.10: Dimensions of the steel (left) and concrete (right) beams used to determine

representative structural responses to the varying temperature distributions.

The thermal response of each beam was calculated for a variety of temperature-time

curves above the mean. This information was used in conjunction with thermal

definitions of fire resistance based on assumed critical temperatures for each

material. Each curve was generated from each experimental data set, starting with

the average compartment temperature-time curve, and then adding a fraction of the

standard deviation to it, in units of one quarter of the standard deviation. Thus, the

first curve analysed for each beam from a given experiment was the average

compartment temperature-time curve. The next curve used was the average

compartment temperature-time curve plus one quarter of the standard deviation,

then the average compartment temperature-time curve plus one half of the standard

deviation, and so on until the average compartment temperature-time curve plus

two times the standard deviation. Figure 2.11 illustrates this by showing every

second curve used for Cardington 2.

400mm

300mm

30mm

32mm dia

16mm dia

8mm dia

Not to scale

15mm

15mm

8mm

200mm

350mm

Page 53: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

33

Figure 2.11: Temperature-time curves for Cardington Test 2, ranging from the average

temperature-time curve (representing the 50th percentile) to the average

temperature-time curve plus two standard deviations (representing the 97th

percentile). Note that this plot only shows every other curve used for structural

assessment.

This approach allows the results to be viewed continuously from the average

compartment temperature-time curve through to the average compartment

temperature-time curve plus two standard deviations. This span, if viewed

cumulatively, covers the range between the 50th percentile and the 97th percentile.

Only values above the mean have been analysed here. This is to focus on the

possibility of current design practices underestimating the effect of fire on structures

by use of the average compartment temperature only. The non-uniformity will also

result in some elements of structure exposed to less severe conditions than currently

assumed using the compartment average. This is not considered here, as a common

aim of structural fire engineering is to err on the side of conservatism.

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Tem

pe

ratu

re (°

C)

Time (min)

Avg (50th Percentile)

Avg + 0.5σ (69th Percentile)

Avg + 1σ (84th Percentile)

Avg + 1.5σ (93rd Percentile)

Avg + 2σ (97th Percentile)

Page 54: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

34

From the percentile temperature-time ranges developed, the peak temperature rise

and time to failure, based on an assumed critical temperature, were calculated for

each beam and each fire test as a function of the temperature percentile. The

unprotected steel beam temperature was calculated by lumped mass heat transfer,

as given by Buchanan [30]. The protected steel beam temperatures were also

calculated by the lumped mass method given by Buchanan. For the concrete beam,

the temperature calculated was that of the internal steel reinforcing bars, assumed to

be at the same temperature as the concrete adjacent to it, i.e. the temperature at the

extreme underside of the bars. This in-depth temperature of the concrete was

calculated with a one-dimensional finite-difference method in explicit form, as given

by Incropera et al. [31].

The time to failure is taken as the time for the steel to heat to 550°C, as this is

normally considered an approximate temperature above which steel loses sufficient

strength such that failure of a typical simply-supported beam could occur under the

loads assumed to be applied during a fire [5]. Higher temperatures are sometimes

used; however 550°C is selected here for the purpose of these calculations, for both

steel beam and rebar temperatures.

A full description of the calculation methods used is given in Appendix A. It is

acknowledged that the calculations and failure criterion are simplistic, and it is

important to note that the illustrative approach taken herein does not account for

several important issues related to the heating and ultimate response of the

structure.

Normalised results for the maximum temperature rise reached against the

temperature percentile are shown in Figure 2.12 for all three beam types. The

normalised temperature rise, ∆′, is defined as the steel temperature rise when

exposed to the given temperature percentile curve divided by the steel temperature

rise when exposed to the average temperature-time curve. The resultant hotter steel

Page 55: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

35

temperature would not be calculated if only the average compartment temperature

were considered. The standard fire is included using the normalised standard

deviation in Eq. (2.1) to generate the full range of temperature-time curves. For

guiding purposes, note that if the gas phase were completely homogeneous, a

horizontal line at ordinate 1 would be shown.

The results show that the increased temperatures associated with the non-

uniformity have a potentially important impact on the structural performance of the

beams analysed. Tables 2.3 through 2.5 show the results for temperature rise and

time to failure for the 80th percentile temperature-time curves (equivalent to the

average compartment temperature-time curve plus 0.85 times the standard

deviation) for each experiment and the standard fire when compared to the average

compartment temperature-time curve. Note that 80th percentile values are often

recommended in fire safety engineering for design. For example, in the UK PD7974

recommends fire loads for structural fire analysis to be the 80th percentile values

[32].

Compared to the calculations using the average compartment temperature

measurements, the results at the 80th percentile show that a higher temperature

region in a compartment could result in a steel temperature rise up to 25% higher

(15% for the unprotected steel beam, 18% for the protected steel beam, and 25% for a

concrete beam) or reach the time to failure, i.e. the fire resistance time, up to 31%

faster (31% for the unprotected steel beam, 15% for the protected steel beam, and

22% for the concrete beam). For the 95th percentile, temperature rises can be up to

60% higher and fire resistance times 55% shorter.

Page 56: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

36

Figure 2.12: Results of the normalised temperature rise for each type of beam analysed.

Note that a horizontal line at abscissa 1 would represent a homogeneous

temperature field.

1

1.1

1.2

1.3

1.4

1.5

1.6

50 60 70 80 90 100

ΔT

' (°° °°C

/ °° °°C

)

Temperature Percentile

Unprotected Steel

Dalmarnock

Cardington F

Cardington F+B

Standard Fire

1

1.1

1.2

1.3

1.4

1.5

1.6

50 60 70 80 90 100

ΔT

' (°° °°C

/ °° °°C)

Temperature Percentile

Protected Steel

1

1.1

1.2

1.3

1.4

1.5

1.6

50 60 70 80 90 100

ΔT

' (°° °°C

/ °° °°C

)

Temperature Percentile

Concrete

Page 57: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

37

Temperature Rise Time to Failure

Test Difference % Increase Difference % Decrease

Dalmarnock Test One 96°C 15% 3.8 min 26%

Cardington 1 91°C 11% 4.5 min 21%

Cardington 2 87°C 8% 1.0 min 6%

Cardington 3 84°C 8% 1.1 min 15%

Cardington 4 44°C 4% 0.5 min 5%

Cardington 5 61°C 5% 0.5 min 5%

Cardington 6 44°C 4% 0.7 min 4%

Cardington 7 59°C 5% 0.5 min 8%

Cardington 8 109°C 10% 0.9 min 9%

Standard Fire 81°C 8% 3.1 min 31%

Table 2.3 Summary of the unprotected steel beam results for temperature rise and time to

failure for the 80th percentile temperature-time curve.

Temperature Rise Time to Failure

Test Difference % Increase Difference % Decrease

Dalmarnock Test One 30°C 18% Did not fail Did not fail

Cardington 1 43°C 12% Did not fail Did not fail

Cardington 2 51°C 8% 5.2 min 10%

Cardington 3 59°C 10% 5.6 min 12%

Cardington 4 29°C 5% 3.1 min 7%

Cardington 5 36°C 6% 6.4 min 13%

Cardington 6 25°C 4% 2.6 min 5%

Cardington 7 31°C 5% 3.7 min 9%

Cardington 8 52°C 9% 5.3 min 11%

Standard Fire 71°C 10% 8.9 min 15%

Table 2.4 Summary of the protected steel beam results for temperature rise and time to

failure for the 80th percentile temperature-time curve.

Temperature Rise Time to Failure

Test Difference % Increase Difference % Decrease

Dalmarnock Test One 47°C 25% Did not fail Did not fail

Cardington 1 53°C 14% Did not fail Did not fail

Cardington 2 60°C 10% 7.0 min 13%

Cardington 3 67°C 12% 6.5 min 15%

Cardington 4 34°C 6% 2.8 min 8%

Cardington 5 48°C 9% 5.6 min 14%

Cardington 6 33°C 5% 2.5 min 6%

Cardington 7 40°C 7% 3.0 min 9%

Cardington 8 66°C 11% 6.7 min 15%

Standard Fire 63°C 9% 15.3 min 22%

Table 2.5 Summary of the concrete beam results for temperature rise and time to failure

for the 80th percentile temperature-time curve.

Page 58: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

38

With respect to the heat transfer analysis, the methods used are analogous to those

employed for uniform temperature fields, but because they are applied to a range of

temperature-time curves above the compartment average, the cumulative results

provide insight into the possible heating from heterogeneous temperature fields. It

is noted that fully spatially resolved heat transfer analyses, as described by Jowsey

[28], were not conducted. That type of analysis could be applied to calculate the

non-uniform heating from a heterogeneous temperature field, but requires spatially

resolved optical properties and velocities of the combustions gases, which were not

available for all of the tests reviewed in this paper.

In terms of the structural behaviour, only a single element has been considered with

a fixed temperature representing the failure criterion, thus the method ignores a

range of possible structural behaviours including axial restraint, membrane actions,

and flexural continuity over multiple spans in a real building. Many more detailed

methods and criteria exist to determine the impact of fire on structures for defining

their fire resistance [30]. However, given that generic structural elements are being

assessed for illustrative purposes only, the current analysis provides useful insights.

Although not assessed here, the location of the thermal non-homogeneities along a

structural member is potentially important, since localised heating in regions of

lower applied stresses may be less critical for structural performance than in regions

of high applied stress. A more detailed structural analysis accounting for thermal

non-homogeneities would be required to investigate the potential impacts of non-

uniform heating on full frame response to fire.

2.5 Conclusions

The statistical analyses of the fire tests examined show that there is considerable

non-uniformity in the temperature fields of real post-flashover fires. Peak local

temperatures range from 23% to 75% higher than the compartment average, with a

Page 59: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

39

mean peak increase of 38%. Local minimum temperatures range from 29% to 88%

below the spatial average, with a mean local minimum temperature of 49% below

the compartment average. This is in contrast to the common assumption of a

homogeneous temperature field often used in quantification and modelling of post-

flashover compartment fires.

The contradictions between the assumption of homogeneity and measured

heterogeneity means that fire tests with limited spatial instrumentation, which are

often only reported as average temperature measurements, may lead to erroneous

conclusions. If fire tests are not well instrumented, it may be difficult to determine

which portion of the temperature distribution has been measured and which parts

were not recorded. It has been shown here with the data from the most densely

instrumented experiments to date that this range is on the order of hundreds of

degrees Celsius.

This heterogeneity can have a potentially non-negligible impact on the structural

fire resistance of steel or concrete beams. This is noticeable in increased structural

temperatures (up to 25% higher) and shorter times to failure (up to 31% faster) at the

80th percentile values compared to those that would be calculated assuming the

average compartment temperature. These results along with the recent studies

showing some structural elements are adversely affected by temperature gradients

gives motivation to revisit the homogeneous temperature assumption and further

explore its ramifications.

While the full implications of the temperature heterogeneity of post-flashover fires

are not explored here, it is apparent that post-flashover fires do not reach uniform

conditions. The presented results highlight the need to increase the spatial

resolution of measurements in fire experiments to capture the full variation within

the compartment. Spatially resolved data can lead to a rational statistical approach

Page 60: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

40

to fire behaviour when applied to fire safety and structural engineering

applications.

References

1 Karlsson, B. and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.

2 Thomas. P.H., “Modelling of compartment fires,” Fire Safety Journal, Vol. 5,

1983, pp. 181 – 190.

3 Magnusson, S.E. and Thelandersson, S., “Temperature-time curves for the

complete process of fire development — a theoretical study of wood fuels in

enclosed spaces,” Acta Polytechnica Scandinavica, Stockholm, Vol. Ci 65, 1970.

4 Babrauskas, V. and Williamson, R.B., “Post-flashover compartment fires: Basis

of a theoretical model,” Fire and Materials, Vol. 2, 1978, pp. 39–53.

5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.

6 Franssen, J.M. “Improvement of the parametric fire of eurocode 1 based on

experimental test results,” Proceedings of the 6th International Symposium on Fire

Safety Science, pp. 927–938, 1999. doi:10.3801/IAFSS.FSS.6-927.

7 ISO 834-1: Fire-resistance tests - Elements of building construction, Part 1: General

Requirements. ISO, 1999.

8 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:

Method for Determination of the Fire Resistance of Elements of Construction:

BSI, 1987.

9 ASTM E119 - 08a, Standard Test Methods for Fire Tests of Building Construction and

Materials. ASTM, 1987.

10 Keltner, N.R., Beck, J.V., and Nakos, J.T., “Using directional flame

thermometers for measuring thermal exposure,” ASTM E5 - Advances in the

State of the Art of Fire Testing, Miami, Florida, 2008.

11 Harmathy, T.Z., “Postflashover fires - an overview of the research at the

national research council of canada (nrcc), 1970-1985,” Fire Technology, vol. 22,

pp. 210–233, Aug. 1986.

Page 61: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

41

12 Bøhm, B. and Hadvig, S., “Nonconventional fully developed polyethylene and

wood compartment fires,” Combustion and Flame, vol. 44, no. 1-3, pp. 201 – 221,

1982.

13 Welch, S., Jowsey, A., Deeny, S., Morgan, R., and Torero, J.L., “BRE large

compartment fire tests–characterising post-flashover fires for model

validation”. Fire Safety Journal, vol. 42, pp. 548 – 567, 2007.

14 Abecassis-Empis, C., Reszka, P., Steinhaus, T., Cowlard, A., Biteau, H., Welch,

S., Rein, G., and Torero, J.L., “Characterisation of Dalmarnock fire test one,”

Experimental Thermal and Fluid Science, Vol. 32, pp. 1334 – 1343, 2008.

15 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,

“Natural Fires in Large Scale Compartments”, British Steel, 1994.

16 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation

Openings – Comparison of Long and Wide Enclosures,” The 6th International

Symposium on Fire Safety Science, Poitiers, France, 1999.

doi:10.3801/IAFSS.FSS.6-941.

17 Thomas, I., Moinuddin, K., and Bennetts, I., “Fire development in a deep

enclosure,” The 8th International Symposium on Fire Safety Science, Beijing, China,

2005.

18 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,

Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the

World Trade Center Towers. NIST NCSTAR 1-5, 2005.

19 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,

Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire

Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST

NCSTAR 1-9, 2008.

20 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based

analysis of a concrete building subjected to fire,” Advanced Research Workshop on

Fire Computer Modelling, Santander, Spain, 2007,

http://www.era.lib.ed.ac.uk/handle/1842/1988.

Page 62: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

42

21 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT

Instituut voor Veilingheids – en Crisismanagement, 2008.

22 Steckler, K.D., Quintiere, J.G., and Rinkinen, W.J., Flow Induced by Fire in a

Compartment. NBSIR 82-2520, 1982.

23 Rein, G., Abecassis-Empis, G., and Carvel, R. Eds., The Dalmarnock Fire Tests:

Experiments and Modelling. School of Engineering and Electronics, University of

Edinburgh, 2007.

24 Lennon, T. and Moore, D., “The natural fire safety concept - full-scale tests at

Cardington,” Fire Safety Journal, Vol. 38, 2003, pp. 623 – 643.

25 Internal Report, Arup Fire, San Francisco. 2009.

26 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and

Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th

International Interflam Conference, London, UK, 2007.

http://www.era.lib.ed.ac.uk/handle/1842/1980

27 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach

to design fires for structural analysis of non-conventional buildings: A case

study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,

http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf

28 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, The

University of Edinburgh, 2006, http://www.era.lib.ed.ac.uk/handle/1842/1480.

29 Gillie, M., Röben, C., Ervine, A., and Kirkpatrick, S., “The effects of non-

uniform fires on structural behaviour,” Proceedings of the Fith International

Conference on Structures in Fire, Singapore, 2008.

30 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.

31 Incropera, F., DeWitt, D., Bergman, T., and Lavine, A., Fundamentals of Heat and

Mass Transfer. John Wiley & Sons, 2007.

32 PD7974-0:2002 Application of fire safety engineering principles to the design of

buildings — Part 0: Guide to design framework and fire safety engineering procedures.

BSI, 2002.

Page 63: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

43

3 A Review of Travelling

Fires in Structural Analysis

3.1 Introduction

As architectural trends change and become more ambitious, they challenge the

bounds of traditional engineering methods. This is true for structural fire

engineering, where the fire scenarios most commonly used for the design of modern

buildings are based on traditional methods that assume uniform burning and

homogeneous temperature conditions throughout a compartment, regardless of its

size.

However, close inspection of accidental fires in large, open-plan compartments

reveals that they do not burn simultaneously throughout the whole enclosure.

Instead, these fires tend to move across floor plates as flames spread, burning over a

limited area at any one time. These fires have been labelled “travelling fires”.

Page 64: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

44

The uniform burning and homogeneous temperature assumptions are at the root of

many of the existing methods’ limitations and have not been confirmed

experimentally for large compartments. The traditional methods were developed

based on small scale tests and, while they are known be of some validity for small

compartments, cannot be readily applied to large enclosures.

Developing new methods to enhance optimisation of structural fire design, by

obtaining a more accurate characterisation of actual building performance, requires

a realistic definition of potential fire scenarios. Specifically, incorporation of

travelling fires will be necessary to reflect the state-of-the-art knowledge of fire

dynamics in large spaces.

This paper reviews research focused on travelling fires in structural analysis. It

highlights the historical developments as well as current uses and examines both the

definition of the thermal environment as well as structural analyses based on

travelling fires.

3.2 Traditional Design Methods

The earliest attempts of testing to understand structural performance in fire led to

the standard temperature-time curve, first published in 1917 [1]. This curve and

associated test methods given in standards, such as BS 476 [2], ISO 834 [3], and

ASTM E119 [4], have formed the basis for the fire rating systems in most building

codes and standards worldwide. The curve came from collating the results of

various post-flashover fire tests into one idealised curve. The tests that fed into the

development of the standard fire were intended to represent worst case fires in

enclosures to determine if the structure could withstand burnout. However, these

tests were conducted and the standard fire created prior to much scientific

understanding of fire dynamics. Thus the standard fire, unlike a real fire, has a

Page 65: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

45

relatively slow growth rate (which was largely driven by the usage of furnaces

heated by manually stoked wood fuel [1]), never reduces in temperature due to fire

decay, and is independent of building characteristics such as geometry, ventilation

and fuel load [1, 5, 6]. Furthermore, the standard fire does not accurately reflect the

nature of real fires which do not uniformly heat building elements [7].

As fire science matured, models of post-flashover fire behaviour were developed to

account for a better understanding of compartment fire dynamics based on tests

conducted in small enclosures. Most of the theoretical models developed were

based on the assumption of uniform compartment temperatures [8]. This is the case

for both analytical models and zone models. Karlsson and Quintiere [9] note that

this assumption, among others, is required for an analytical solution of the energy

balance for the compartment. In particular they note that the methods of

Magnusson and Thelandersson in 1970 [10] and Babrauskas and Williamson in 1978

[11] adopted this approach.

Pettersson et al. [12] developed a design guide, based on the work of Magnusson

and Thelandersson [10], for specifying the thermal environment to be used for

structural design. The guidance document provides a set of temperature-time

curves for various compartment ventilation factors, fuel loads, and compartment

linings. This work was further developed by Wickström [13] and became the basis

for the Eurocode parametric temperature-time curve [14], which is a widely used

method in structural fire engineering today.

While other methods exist [15, 16, 17, 18], they all assume homogeneous

temperature conditions and uniform burning throughout the fire compartment.

Drysdale [5] notes that a justification of the homogeneous temperature assumption

often used is that there is supposedly a small gradient in the vertical temperature

distribution during a post-flashover fire and even smaller horizontal gradients. For

example, a single test from 1975 is cited showing a nearly uniform vertical

Page 66: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

46

temperature distribution at one moment at the onset of flashover. Section 3.3 of this

paper presents further critiques of this assumption.

While most of the traditional methods tend to look at full compartment

involvement, some methods have been developed to look at localised fires [14, 19]

that look at the impact of a fire on only part of a structure. Considering localised

fires is a relaxation of the uniform burning assumption. This is relevant to this

review paper, as a travelling fire is, in essence, a localised fire that moves. Howver,

the methods developed for localised fires have not considered elevated smoke

temperatures away from the fire as methods for travelling fires have (see Section

3.4).

Buchanan [20] and Law et al. [21] provide concise histories of the development

structural analysis methods for buildings exposed to fires. What is of relevance to

this review is the move from solely analysing single elements to that of whole frame

behaviour, which was largely driven by specific accidental fires and large scale

testing at Cardington. Travelling fires, which provide highly non-uniform and

transient heating in time over the full length of a large compartment, may have a

considerable impact on whole frame structural behaviour.

3.3 Limitations of the Uniform Burning

Assumption

The traditional methods have known limitations in their application. For example,

Eurocode 1 states that the parametric curves are only valid for compartments with

floor areas up to 500m2 and heights up to 4m, the enclosure must also have no

openings through the ceiling, and the compartment linings are restricted to having a

thermal inertia between 1000 and 2200J/m2s½K, which means that highly conductive

linings such as glass façades and highly insulating materials cannot be taken into

account. As a result, common features in modern construction like large enclosures,

Page 67: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

47

high ceilings, atria, large open spaces, multiple floors connected by voids, and glass

façades are excluded from the range of applicability of the current methodologies.

A recent survey of buildings in Edinburgh, UK [22], underlines the implications of

these limitations on the applicability of design fires, particularly for modern

structures. For buildings built over a long period of time starting in the early 20th

century, 66% of their total volume falls within the limitations. However, in a newly

constructed, modern building that has open spaces and glass façades, only 8% of the

total volume is within the limitations. This suggests that modern building design is

increasingly producing buildings that contain compartments to which parametric

fires should not be applied.

Furthermore, as noted in Section 3.2, the traditional design methods for specifying

the thermal environment for structural analysis are based on an assumption of

uniform burning and temperature conditions. Stern-Gottfried et al. [23] have

reviewed this assumption by analysis of existing experimental data from well-

instrumented fire tests. Results show that dispersion from the spatial compartment

average is significant and that the assumption of uniform temperature conditions

does not hold well (see Section 3.3.1 for more details). While this review was

conducted for relatively small enclosures, the findings are likely to be more relevant

for large enclosures as the compartment size increases, the degree of heterogeneity

is expected to increase.

It is worth noting that the traditional methods assume that worst case conditions are

caused by ventilation controlled fires. However, a recent review by Majdalani and

Torero [24] of early CIB tests and the resulting analyses of compartment fire

behaviour done by Philip Thomas and others highlights that ventilation controlled

fires are unlikely in large enclosures and that they are not necessarily more

conservative for structural analysis than fuel bed controlled fires. Majdalani and

Torero note that while the different burning behaviour between ventilation and fuel

Page 68: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

48

bed controlled fires was clearly stated in the original studies, ventilation controlled

fires have nonetheless been assumed to be the most severe case for design.

Buchanan [6] notes that post-flashover fires in open plan offices are unlikely to burn

throughout the whole space at once. Although limited experimental data exist on

fire spread and temperature homogeneity in large enclosures, examination of

specific tests and the study of accidental fires can provide insight into the fire

dynamics of larger enclosures.

3.3.1 Evidence from Experiments

The well instrumented tests conducted at Dalmarnock [25] and Cardington [26]

were shown to have large standard deviations (in excess of 200°C at times) within

the temperature field [23]. Additionally, peak local temperatures in these tests were

found to vary from 23% to 75% above the compartment spatial averages, and local

minimums ranged from 29% to 88% below the averages.

Kirby et al. [27] ran a test series burning wood cribs in a long enclosure with

approximate dimensions of 22.9m x 5.6m x 2.8m. All of the tests were ignited at the

rear of the compartment, except one in which all wood cribs were ignited

simultaneously. The results of all tests showed that the fire moved relatively quickly

from the ignition location to the front of the compartment, where the vent was

located. After the fuel in the front of the compartment burnt out, the fire

progressively travelled back into the compartment and ultimately consumed all of

the fuel and self-extinguished at the rear. Temperature results at the rear, middle

and front of the compartment of Test 1 from this series are shown in Figure 3.1.

Thomas and Bennetts [28] conducted a test series of ethanol pool fires in a small

rectangular enclosure (1.5m x 0.6m x 0.6m) to determine the influences of ventilation

size and location on burning rate. They found that there were significant differences

in burning rates between having the opening on the short end (long enclosure) or

Page 69: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

49

the long side (wide enclosure). They observed temperature differences across

multiple locations of up to 500°C, generally with greater temperatures nearer the

vents, as this is where the flames resided more often. This work was continued

further [29] with another experimental series of pool fires in a larger, long enclosure

(8m x 2m x 0.6m), in which the opening size on the short end was varied. The results

obtained were similar to both their earlier work [28] and that of Kirby et al. [27].

They conclude that a structural element near the vent would be exposed to more

severe conditions than one further inside the compartment.

Figure 3.1: Comparison of temperature measurements over time at three different locations

from the rear to the front of the compartment, illustrating non-uniform burning

of the wood cribs during the tests of Kirby et al. [27].

All of the tests mentioned here show, even in relatively small scales, that fires travel

and do not burn uniformly throughout the whole test enclosure.

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Tem

pe

ratu

re (°

C)

Time (min)

Rear

Middle

Front

Page 70: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

50

3.3.2 Evidence from Accidental Fires

Many large, accidental fires, such as those in the World Trade Center Towers 1, 2

[30] and 7 [31] in New York in September 2001, the Windsor Tower in Madrid,

Spain in February 2005 [32] and the Faculty of Architecture building at TU Delft in

the Netherlands in May 2008 [33] were all observed to travel across floor plates, and

vertically between floors, rather than burn uniformly for their duration. Similar

observations were made of the Interstate Bank fire in Los Angeles in 1988 [34] and

the One Meridian Plaza fire in Philadelphia in 1991 [35].

The travelling nature of the fire in Tower 2 at the World Trade Center is shown in

Figure 3.2, which gives the recorded observations of the fire location and burning

behaviour along the East Face [30]. It can be seen that the area of flaming shifts

dramatically on the floors of fire involvement, both horizontally across floors as well

as vertically between floors.

Other than the fires in Towers 1 and 2 of the World Trade Center, which ended at

the time of building collapse, all of the incidents listed above lasted for many hours.

The Interstate Bank fire was the shortest and lasted a little under four hours, at

which point it was controlled by fire fighters. The One Meridian Plaza fire was the

longest, which lasted for almost 19 hours as it burnt from the 22nd to the 30th floor,

where it was eventually controlled by a sprinkler system.

These fires, in addition to being visually observed as travelling, had durations that

are well in excess of the time periods associated with the traditional design

methods. This difference in time scales is primarily due to those methods assuming

uniform burning on one floor only. Therefore the traditional methods may be

underestimating exposure times as compared to the lengths of real fires, which in

turn could affect the structural heating.

Page 71: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

51

Figure 3.2: Observed fire locations over different time periods on the East Face of WTC

Tower 2 [30], indicating a horizontally and vertically travelling fire.

Blue = observation not possible, White = no fire, Yellow = spot fire, Red = fire

visible inside, Orange = external flaming.

3.4 Pioneering Methods

To progress past the limitations of the traditional methods, it is necessary to develop

engineering techniques that account for travelling fires. This section reviews the

published methods utilising travelling fires.

3.4.1 Large Firecell Method - HERA New Zealand

As part of a long term research programme at HERA in New Zealand aimed at

understanding the behaviour of complete steel frames exposed to fire, Clifton [36]

produced a first of its kind report related to design using travelling fires. The report,

entitled “Fire Models for Large Firecells” and referred to as the Large Firecell

Page 72: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

52

Method (LFM) in this paper, gave an approach to apply specific fire models to

develop temperature-time relationships for travelling fires through a “firecell”. By

Clifton’s definition, a firecell is essentially one compartment of a building. For

example, an open plan office floor would be a single firecell.

Clifton applied two different fire models to generate temperature-time curves and

created a set of rules on how these should be applied to “design areas” within the

firecell. Each design area of the firecell at any one time could be classified as one of

the following conditions: fire, preheat, smoke logged, or burned out. This is

illustrated in Figure 3.3 at a fixed moment in time.

Figure 3.3: Representation of a spreading fire in the LFM [36]. Reproduced with permission

from the author.

The temperature-time curves for the design areas were calculated by one of two

models given, both for ventilation controlled fires. Temperatures for the preheat and

delayed cooling (for after burnout) periods were taken to be between 200 and 675°C,

depending on the type of construction used in the first version of the report and

then subsequently modified to 400 to 800°C in the proposed changes to the

document.

Page 73: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

53

In the first version of the LFM, Clifton set the size of each design area based on the

fuel load density. He suggested 50m2 for a fuel load under 500MJ/m2, 100m2 for fuel

loads between 500 and 1000MJ/m2, and 150m2 for fuel loads greater than 1000MJ/m2.

This was modified to have the design area be 50m2 for all fuel loads in the proposed

changes. Windows were assumed to break once the adjacent gas temperature

reached 350°C. The rate of fire spread was based on the Kirby experiments [27]

highlighted in Section 3.3.1 and was specified to be 1m/s for well ventilated

conditions and 0.5m/s for less ventilation, as determined by the opening factor of

the case being examined.

Combining all of the various inputs in the method gives temperature-time curves at

any structural element. An example is shown in Figure 3.4.

Clifton acknowledged the challenges of developing this type of methodology. He

stated that no such method existed before and that there was a “paucity of

experimental data available”, which required “a crude and simplistic approach to

their development”. Therefore the model necessitated numerous assumptions

regarding fire size, ventilation conditions, fire spread, fuel distribution and fuel

type. Due to the assumptions needed, and the lack of experimental data, Clifton

stated that the LFM should mostly function as a research tool and should only be

used for single element checks in design.

Moss and Clifton [37] used the LFM in analysis of the large frame tests conducted at

Cardington. However, they noted that this method, combined with detailed

structural analyses led to results “that appeared to be realistic,” but “could not be

related to any directly comparable experimental results”. Further development or

applications of this method are not readily apparent in the literature.

Page 74: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

54

Figure 3.4: Temperature-time curve of one design area in the LFM [36]. Reproduced with

permission from the author.

3.4.2 Travelling Fires Methodology – University of Edinburgh

The Travelling Fires Methodology (TFM), which has been developed by the authors

independently of the LFM over the last few years, incorporates travelling fires for

structural design. Full details of this method are given in Chapter 5 [38].

The TFM calculates the fire-induced thermal field such that it is physically-based,

compatible with the subsequent structural analysis, and accounts for the fire

dynamics relevant to the specific building being studied. In order to achieve this, a

fire model is selected that provides the spatial and temporal evolution of the

temperature field.

The fire-induced thermal field is divided in two regions: the near field and the far

field. These regions are relative to the fire, which travels within the compartment,

and therefore move with it. The near field is the burning region of the fire and

where structural elements are exposed directly to flames and experience the most

Page 75: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

55

intense heating. The far field is the region remote from the flames where structural

elements are exposed to hot combustion gases (the smoke layer) but experience less

intense heating than from the flames. The near and far fields are illustrated in Figure

3.5. The near field region is analogous to the design area of the LFM.

Figure 3.5: Illustration of near and far fields in the TFM [38, 42].

Early work on the TFM in 2006 by Rein et al. [39] used Computational Fluid

Dynamics (CFD) to study both uniform and travelling fires in a multi-storey high

rise building, with atria connecting groups of three floors into “villages”. Later work

by Stern-Gottfried et al. [40] simplified and refined the method for a single floor,

utilising a ceiling jet correlation to generate far field temperatures. Jonsdottir et al.

[41] took this updated version and examined resultant steel temperatures.

Collaboration with structural fire engineers led to work [42] exploring the response

of a generic concrete frame to travelling fires, including a detailed sensitivity study.

Stern-Gottfried and Rein [38] then developed the methodology further by extending

the examination of the concrete frame via simplified heat transfer and identified the

critical parameters for applying the method to design.

The TFM does not assume a single, fixed fire scenario but rather accounts for a

whole family of possible fires, ranging from small fires travelling across the floor

plate for long durations with mostly low temperatures to large fires burning for

Far field (Tff) Near field (Tnf)

Near field

travels over

time

Page 76: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

56

short durations with high temperatures. Using the family of fires enables the TFM to

overcome the fact that the exact size of an accidental fire cannot be determined a

priori. This range of fires allows identification of the most challenging heating

scenarios for the structure to be used as input to the subsequent structural analysis.

Each fire in the family burns over a specific surface area, denoted as ��, which is a

percentage of the total floor area, �, of the building, ranging from 1% to 100%.

Compared to this approach, the conventional methods only consider full size fires,

which are analogous to the 100% fire size in the TFM. All other burning areas

represent travelling fires of different sizes which are not considered in the

conventional methods.

The TFM assumes that there is a uniform fuel load across the fire path and the fire

will burn at a constant heat release per unit area typical of the building load under

study. From this the total heat release rate can be calculated by Eq. (3.1).

� = ��� " (3.1)

where � is the total heat release of the fire (kW)

�� is the floor area of the fire (m2)

� " is the heat release rate per unit area (MW/m2)

Furthermore, the local burning time over the fire area can be calculated by Eq. (3.2).

"# = $�� " (3.2)

where "# is the burning time (s)

$� is the fuel load density (MJ/m2)

Page 77: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

57

Values typically used in the application of the TFM are 570MJ/m2 for the fuel load

density and 500kW/m2 for the heat release rate per unit area. This leads to a

characteristic burning time, "#, of 19min. This time correlates well to the free-

burning fire duration of domestic furniture, which Walton and Thomas [43] note is

about 20min. It is also in line with Harmathy’s [44] observation that fully developed,

well ventilated fires will normally last less than 30min.

Note that the burning time is independent of the burning area. Thus the 100%

burning area and the 1% burning area will both consume all of the fuel over the

specified area in the same time, "#. However, a travelling fire moves from one

burning area to the next so that the total burning duration across the floor plate is

extended. This means that there is a longer total burning duration for fires with

smaller burning areas.

As noted above, the TFM splits the temperature field into two portions: the near

field (flaming region) and the far field (hot gases away from the fire). In the case of

the 100% burning area, all of the structure will experience near field (flame)

conditions for the total burning duration (which is equal to the burning time, "#).

However, for the travelling fire cases, any one structural element will feel far field

(smoke) conditions for the majority of the total burning duration and near field

conditions for the burning time when the fire is local to the element. Therefore the

TFM must quantify both the near field and far field temperatures.

The TFM assumes the near field is 1200°C to represent worst case conditions, as this

is the upper bound of flame temperatures generally observed in compartment fires

[5]. To calculate the far field temperatures in the TFM, an engineering tool must be

selected and applied to each member of the family of fires developed. The TFM is

modular in this aspect, as any calculation method that takes fire size and geometry

as inputs and produces temperature as a function of distance from the fire may be

used.

Page 78: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

58

As stated above, the early work [39] used a CFD fire model to study the temperature

field as a function of distance from the fire. As the case study for that work involved

an atrium, a detailed three-dimensional model was needed. Indicative results from

the case study are shown in Figure 3.6.

(a) (b)

Figure 3.6: (a) Use of CFD with the TFM in a case study with an atrium; (b) Calculated far

field temperatures for the same case study [39].

Later variations of the TFM [38, 40, 41, 42] focused on a simpler method to obtain far

field temperatures by using a ceiling jet correlation developed by Alpert [45]. This

correlation is given below in Eq. (3.3).

%�& − ∞ = 5.38�� )⁄ �+ ,⁄-

(3.3)

where %�& is the maximum ceiling jet temperature (°C)

. is the ambient temperature (°C)

) is the distance from the centre of the fire (m)

- is the floor to ceiling height (m)

0

300

600

900

1200

-25 -15 -5 5 15 25Distance [m]

Temperature at Ceiling Height [C]]

Page 79: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

59

Note that while Alpert gives a piecewise equation for maximum ceiling jet

temperatures to describe the near field (r/H ≤ 0.18) and far field (r/H > 0.18)

temperatures, only the far field equation is used as the near field temperature is

assumed to be the flame temperature in the TFM. Although it was acknowledged

that the ceiling jet correlation does not fully characterise the fire dynamics of the

scenarios selected, it provided sufficiently accurate results to progress the

development of the TFM.

In order to limit the amount of information passed to the structural analysis, the first

iteration of the TFM by Rein et al. [39] only took a single far field temperature from

a point away from the flaming region (see red lines showing indicative temperature

in Figure 3.6b). Later versions used a fourth power average of temperature for the

far field in a bias towards radiative heat transfer [40, 41, 42]. However, in more

recent work by Stern-Gottfried et al. [38], this assumption has been relaxed and a

spatially resolved temperature field that varies with distance from the fire is used.

Instead of the average, the compartment is divided into discreet nodes, each with

their own temperature. Figure 3.7 shows representative temperature-time curves

developed at a single point for averaged and spatially resolved far field

temperatures.

The TFM provides results of the full temperature field evolution over time, which

can be used to examine particular structural elements or full frame behaviour. The

fire travels at a velocity related to its size. These velocities vary from centimetres per

minute for small fires to metres per minute for large fires, which is a broader range

than that used by Clifton in the LFM. The range of fire sizes examined in the TFM is

deemed to cover the full extent of what is physically possible in an enclosure fire.

Page 80: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

60

Figure 3.7: Temperature-time curves at a single location in the TFM, showing averaged and

resolved far field temperatures.

In the TFM when averaged far fields are used they can be plotted together and

compared to examples of traditional methods. This is shown in Figure 3.8.

It can be seen from the results of the TFM that hotter far field temperatures last for

less time than cooler ones. The standard and parametric temperature-time curves

give similar temperatures to those in the far field from travelling fires of sizes

between 25% and 50% but do not account for the near field conditions like the TFM

does. The results of the standard fire curve cannot be explained after one hour of

burning in terms of the possible fire dynamics in.

0

200

400

600

800

1000

1200

1400

0 50 100 150 200

Tem

pe

ratu

re (o

C)

Time (min)

Averaged

Resolved

Page 81: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

61

Figure 3.8: Averaged far field temperatures for a family of fires in the TFM and traditional

methods as applied to a generic concrete frame 42m x 28m x 3.6m per floor [42].

While a simple plot cannot be shown for a resolved far field, the results can

nevertheless be used for heat transfer and structural analysis. Their results are better

compared to the traditional methods via the resulting structural performance, as

shown in Figure 3.9, which compares rebar heating from exposure to a 10%

travelling fire, the standard fire and two different Eurocode parametric

temperature-time curves.

The temperature fields generated from the TFM have been applied to both concrete

and steel structures by means of heat transfer analyses [38, 41]. These analyses have

looked at the temperature of either steel rebar within concrete or steel beams as a

loose surrogate for structural performance. The results showed that travelling fires

have a significant impact on the performance the structures examined and that

conventional design approaches cannot automatically be assumed to be

conservative. Medium sized fires between 10% and 25% of the floor area were found

to be the most onerous for the structure. This is due to a balance of burning duration

and far field temperatures.

0

200

400

600

800

1000

1200

1400

0.1 1 10 100

Far

Fie

ld T

em

pe

ratu

re (°

C)

Time (hours)

1%

2.5%

5%

10%

25%

50%

100%

Std Fire

EC1 25%

EC1 100%

Page 82: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

62

Figure 3.9: Comparison of rebar temperatures calculated using a 10% fire size from the

TFM, the standard fire, and two Eurocode parametric temperature-time curves

in a similar generic concrete frame as shown in Figure 3.8 [38].

Detailed sensitivity analyses of the input parameters of the TFM have also been

conducted [38, 42], showing that the structural design and fuel load have a larger

impact on structural behaviour than any numerical or physical parameter used in

the methodology.

3.5 Structural Response

In his plenary lecture at the IAFSS Symposium in 2008, Buchanan [20] stated:

The two disciplines of combustion science and structural engineering are miles apart,

so two groups of experts will always be needed. For this reason it would be very foolish

to rush towards coupling of fire models with structural models. Any such coupling

would lead to a “black box” mentality with a major decrease in our ability to make

accurate predictions of structural fire behaviour.

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Ba

y T

em

pe

ratu

re (o

C)

Time (min)

10% Travelling Fire

EC - 25% Ventilation

EC - 100% Ventilation

Standard Fire

10% travelling fire

equivalent to 106 min

Standard Fire

106 min

556oC

56 min38 min

363oC

252oC

Page 83: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

63

Fire engineers and structural engineers need to talk to each other much more than

they do now, and each group needs to learn as much as possible of the other discipline.

These two topics are too big and too different for us to educate combined specialists in

both disciplines.

The comments made by Buchanan, and reinforced by Law et al. [21] highlight the

need for close collaboration between the two disciplines. The TFM has been

developed with such collaboration in mind [38, 39, 40, 41, 42].

This section reviews research involving detailed structural analysis of travelling

fires.

3.5.1 Steel Frame

The first detailed analysis of structural behaviour in response to travelling fires was

conducted by Bailey et al. [46]. This work, which was notably conducted prior to

publication of Clifton’s LFM and twelve years before Buchanan’s call for multi-

disciplinary collaboration, was pioneering in its recognition for the need to consider

the structural impact of a more realistic fire environment than the conventional

methods by examining travelling fires.

Bailey et al. extended use of a Finite Element Model (FEM) from previous research

involving uniform fires to study a two-dimensional frame exposed to a spreading

fire. The work began with a focus on the effect of the cooling phase of a fire on the

structure. The authors then note that incorporating the cooling phase allows

consideration of “fires which spread progressively from an ignition point in a single

compartment (or a zone within an open-plan area) to adjacent areas of the

building”. They go on to state:

The effect of a spreading fire is that both cooling and heating are taking place

simultaneously in different zones. This is arguably a more typical condition than the

assumption that the temperature changes uniformly throughout the fire-affected zone,

and in view of the effects of restraint observed during cooling is one which requires

investigation.

Page 84: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

64

The study compares the response of a two-dimensional bare steel frame exposed to

a spreading fire with that of a uniform fire, over both three and five structural bays.

The uniform fire was defined by a temperature-time curve representing a “natural”

fire. The travelling fire was represented by the same natural fire curve, but offset in

time for the bays of secondary fire involvement. Once the temperature-time curve in

the first bay reached its peak, the fire was assumed to begin in the adjacent bays.

Similarly, the bays of tertiary fire involvement were assumed to ignite when the

temperature-time curve reached its peak in the secondary bays. The temperature-

time curves used are shown in Figure 3.10.

Figure 3.10: Temperature-time curves used by Bailey et al. (adapted from [46]).

While this method replicates the movement of the near field associated with

travelling fires, the use of a temperature-time curve reproduced with a delay does

not capture the far field of a travelling fire, as can be seen by the relevant details

discussed in Sections 3.3 and 3.4 of this paper. The temperature-time curve used

assumes a ventilation controlled fire. However, a fire burning in only one bay of a

structure nine bays wide is unlikely to be ventilation limited, especially in the early

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300

Tem

pe

ratu

re (o

C)

Time (min)

First Bay

Second Bay

Third Bay

Page 85: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

65

durations of the fire, as the air available from the rest of the structure may provide

sufficient oxygen to keep it well ventilated. Additionally, local exposure to flame

temperatures (near field conditions), and not just compartment average

temperatures associated with the calculation methods of ventilation limited fires,

are likely.

Furthermore, this method does not account for elevated smoke temperatures ofg the

far field away from the fire. The temperature in a bay adjacent to the first one

exposed remains ambient until its curve begins at 36min. Given that the bays are 8m

in dimension, it is much more likely that temperatures in the adjacent bay would be

well above ambient at this time. This behaviour could be explained if each bay were

a fully enclosed, fire rated compartment that fails 36min into the fire, however this

is not the scenario described by the authors.

Bailey et al. went on to examine the vertical displacements and axial forces in the

beams of the structure. They found that higher beam displacements occur for the

spreading fire cases than the uniform ones. The authors noted that these conclusions

cannot be readily generalised and further study is required.

3.5.2 Concrete Frame

More recently, and after the publication of the LFM and TFM, two simultaneous

papers on the impact of travelling fires on concrete frames have been published.

Ellobody and Bailey [47] conducted a study of the impact of horizontally travelling

fires on a post-tensioned concrete floor. While this study utilises sophisticated

structural analysis, including a three-dimensional FEM, the fire definition is very

similar to that used by Bailey et al. [46]. Specifically, a base temperature-time curve

is applied to the first bay of heating and is shifted in time to provide the heating of

bays that become subsequently involved in the fire. In this study, the base

Page 86: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

66

temperature-time curve was taken from Eurocode 1. Two time delays were

examined; one of 64min and another of 30min.

The structural response was viewed in terms of tendon temperatures, deflections

and axial displacements. These parameters were examined at several critical

locations over time as well as in terms of their final residual values. Ellobody and

Bailey noticed that the “change in heating/cooling scenarios between zones resulted

in cyclic deflection patterns at some locations”. They also found that the time delay

used for shifting the temperature-time curve had an impact on the structural

response and the worst case could result from a uniform heating case or a non-

uniform travelling fire. The authors recommended that engineers consider a range

of travelling fires for use in structural design to ensure the most onerous scenario is

found.

Given a very similar method for thermal definition was used in this paper as Bailey

et al. the same critiques of the that method apply; namely the inherent assumption

of a ventilation limited fire in an open space and the lack of consideration of the far

field (hot smoke away from the fire). In fact, the cyclic deflection patterns observed

by Ellobody and Bailey could be affected by the presence of elevated far field

temperatures. This is because in their analysis some elements would be exposed to

ambient gas phase conditions while others to peak temperatures, when in reality the

ambient exposure would more likely have been that of smoke temperatures on the

order of several hundred degrees Celsius.

The work of Law et al. [42], a collaborative research project between the fire

engineers Stern-Gottfried and Rein and structural engineers Law and Gillie, applied

the TFM to a generic concrete frame 42m long x 28m wide. The temperature field

was generated as explained in Section 3.4.2 and then applied to a FEM of the

concrete frame.

Page 87: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

67

The structural modelling results were examined in terms of rebar temperature,

sagging tensile strain, hogging tensile strain, and deflections. The results for rebar

temperature showed that fire sizes between 10% and 25% of the floor area produced

the most onerous results for the structure. All of the more detailed structural metrics

showed that the 25% fire size was most challenging for the structure. In all four

metrics the travelling fires proved to be a worse case for the structure than the

Eurocode parametric temperature-time curves. A detailed sensitivity study showed

that variations in the far field definition and differing fire shapes and paths of travel

had little impact on the results.

In his PhD thesis [48], Law further examined the structural behaviour resulting from

travelling fires, using sectional and utilisation analyses. Generally he obtained

similar results, but did notice that 5% to 10% fire sizes gave the worst case results

for the structure when using a utilisation analysis of all columns. The strength of the

methods applied by Law is that data from numerous fires can be viewed

cumulatively to get a better understanding of the behaviour of each column. This is

well suited to analyse results from the TFM which produces a family of fires.

3.5.3 Vertically Travelling Fires

Noting that large, accidental fires tend to involve multiple floors, Röben et al. [49]

examined the impact of vertically travelling fires on a multi-storey structure. The

building they examined was used in previous work by the authors to understand

the effect of the cooling phase on structural performance and had a concrete core

and a steel-concrete composite floor system.

The study assumed three floors were on fire. Although Röben et al. noted that

“horizontally travelling fires would give a more realistic representation of the fire

spread through a compartment”, the authors assumed horizontally uniform fires for

their study, stating that it is “a common assumption in structural fire design”. The

heating pattern used was similar to the horizontal studies by Bailey et al. and

Page 88: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

68

Ellobody and Bailey, i.e. the same temperature-time curve was applied to each floor

but with a time delay between floors. The heating curve used was a generalised

exponential curve given by Flint [50]. Röben et al. noted that this curve was selected

because analysis by Flint “showed it to be a better approximation for large

compartments than the more commonly used ‘natural fire’ curves given, for

example, in the Eurocodes”, however no theoretical background or physical

justification of the method is given. The cooling phase was assumed to be linear

between the maximum and ambient temperatures over a period of 1400s.

Three fire scenarios were used; uniform heating on all three floors, a time delay of

500s between each floor, and a time delay of 1500s between each floor. The authors

noted that many factors influence the vertical spread rate. The values used in the

study were to roughly capture the range of eyewitness accounts of vertical flame

spread of between 6 and 30min in the Windsor Tower fire.

The results, primarily examined in terms of horizontal displacements of columns

and total axial forces of floors, showed that the vertically travelling fire with a short

time delay induced a similar structural response to that of the uniform heating case.

However, the primary difference observed was a “cyclic pattern induced in

columns” for the travelling fire. This pattern was also observed for the long delay

travelling fire, but with longer time intervals. The authors note that this cyclic

deflection pattern has not been examined before and has a significant impact on the

structure and, therefore, should be considered in design.

The observation of a cyclic pattern is similar to that of Ellobody and Bailey.

However, this finding perhaps has more relevance for vertically travelling fires

because compartment floors will likely limit the spread of hot gases that may

preheat the upper floors prior to full fire involvement. Notwithstanding this

argument, the nature of the column deflections may be affected by consideration of

Page 89: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

69

horizontally travelling fires as well. However, no studies to date have examined

this.

3.6 Practical Applications

The work highlighted so far in this paper have pioneered or developed the concept

of travelling fires and the subsequent structural analyses, which is a research topic

that is beginning to grow within the fire engineering community. This section

reviews recent applications of travelling fires to real building projects found in the

literature.

The first version of the TFM has been applied to case studies in the two real

buildings. These case studies are described below.

In 2009 Stern-Gottfried et al. [40] applied the TFM to the Mumbai C70 building

project, shown in Figure 3.11a, during its early design stages. The building had 13

storeys and was approximately 60m tall. It had a unique structure, including an

external diagrid megaframe consisting of hollow structural steel members designed

to carry wind loads and a proportion of the gravity load, an internal reinforced

concrete core system designed to carry gravity load, and a hat truss at the top of the

building. The exact shape of each floor varied, with most being over 2000m2 in area.

Much of the external façade was glazed, thus placing the building outside the range

of applicability of the traditional design methods.

The 9th floor of the Mumbai C70 building was selected for structural fire analysis, as

this floor had the longest beam spans as well as slender diagrid members compared

to those found lower in the building. Therefore this floor was deemed to be where a

severe fire would be most challenging to the structure and therefore the location

studied. The first version of the TFM was used to generate temperature-time curves,

utilising an averaged far field temperature, specific for the 9th floor. The far field

Page 90: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

70

temperatures plotted against total burning duration for a range of fire sizes for this

study are given in Figure 3.11b, with comparison to the temperature-time curves

from the standard fire and two Eurocode parametric cases.

(a)

(b)

Figure 3.11: (a) Architectural image of Mumbai C70 by James Law Cybertecture; (b) Far

field temperatures vs. total burning durations for different fire sizes, with the

standard temperature-time curve and two parametric Eurocode curves for

reference [40].

0

200

400

600

800

1000

1200

1400

0.1 1 10 100

Far

Fie

ld T

em

pe

ratu

re (°C

)

Time (hours)

1%

2.5%

5%

10%

25%

50%

100%

Std Fire

EC1 25%

EC1 100%

Page 91: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

71

In 2010 Jonsdottir et al. [41] calculated the resultant steel temperatures from a

thermal field generated by the TFM for the Informatics Forum at The University of

Edinburgh, shown in Figure 3.12a. The Informatics Forum was completed and

occupied in 2008. The building was chosen for the study because of its unique

architectural features. It is a seven storey office building for lecturers, staff and

researchers, with a central glass atrium, and a floor area of approximately 1700m2.

The case study examined structural heating of three different steel beams based on

the temperature–time curves of the family of fires generated from the TFM. Example

results of this analysis are given in Figure 3.12b. This paper was the first to report

the resultant structural temperatures caused by travelling fires. These results were

then compared to calculations of the steel beam temperatures utilising the

traditional methods. It was found that the TFM method resulted in 10% to 55%

higher peak steel beam temperatures than the traditional methods for medium sized

fires of 10% to 25% area.

Apart from the LFM and TFM, other researchers have applied similar ideas related

to travelling fires. Sandström et al. [51] developed a pre-processing tool to rapidly

apply travelling fires as input to a CFD model (FDS v5.5). They examined a 20m x

40m x 10m, open plan building with natural ventilation in the roof and on all four

sides. They developed a design fire based on Eurocode 1 [14] guidance, which

ramps up at a “medium” t2 rate, to a peak of 95MW, then linearly decays. This

design fire was then applied using different heat release rates per unit area to define

different fire scenarios, some of which were stationary (covering 12.5% and 100% of

the floor area) and others that were travelling (using fire sizes of 0.125%, 0.5% and

2% of the floor area). It is not clear how the travelling fires were implemented and

no descriptions of the travelling nature, velocity, or burnout characteristics of the

fires were given.

Page 92: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

72

(a)

(b)

Figure 3.12: (a) Informatics Forum at The University of Edinburgh; (b) Resultant steel

temperatures vs. time for three different beam types that were both unprotected

and fire rated to 120min [41].

The results were reported as average smoke layer temperature-time curves,

including comparison to simulations using the two-zone model OZone [18], thus

averaging the near and far fields together into a single temperature. Because of this,

0

100

200

300

400

500

600

700

800

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75

Ste

el T

em

pe

ratu

re (

oC

)

Time (hours)

HE-A 600

HE-A 600 120 min prot.

HE-A 300

HE-A 300 120 min prot.

HE-A 200

HE-A 200 120 min prot.

Page 93: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

73

the analysis more closely resembles the traditional design methods that assume

homogeneous temperature conditions than the travelling fire methods already cited.

In 2010, Shestopal et al. [52] provided a review of two case studies where travelling

fires were implemented with CFD (FDS v5). The authors stated that the worst case

scenarios resulted from a spreading fire, which they used to justify the reduction of

fire resistance levels against those nominally required by the local building code.

The case studies presented were for a supermarket and an office building. In the

supermarket case study, the travelling nature of the fire was modelled via flame

spread predictions within the CFD model. In the office case study it was represented

by user specified sequential ignition along the floor (with time delays ranging from

45 to 90s) set to match experimental heat release rate data.

From the limited information presented, it appears the analyses for the supermarket

may have extended beyond the capabilities of current CFD models, by predicting

flame spread which is a challenging physical process to accurately model [25].

However, the spirit of this work, which examined spatially varying far field

temperatures, is in line with the ethos of the travelling fires methods.

3.7 Conclusions

The concept of travelling fires suggests a paradigm shift in structural fire

engineering. The dynamics of travelling fires are central to better understanding the

true structural performance of buildings exposed to real fires, and therefore the

potential to enable architectural innovation and structural optimisation.

However, given the importance of travelling fires, there has been only a limited

amount of research to date on the topic and more is needed. The earliest research by

Clifton and Bailey et al. in 1996 established the need for robust methods to account

for travelling fires. The development of the TFM in 2006 offers such an engineering

Page 94: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

74

technique. However, refinements to the TFM for horizontally travelling fires are

needed to make it more robust. Additionally, fundamental work is needed to

examine vertically travelling fires. As opposed to horizontally travelling fires, no

framework exists to explore the dynamics of vertically travelling fires, which is

currently hindering their application in structural analysis, despite the numerous

incidents of vertically travelling accidental fires.

Of particular importance in the development and application of travelling fire

methodologies is the close collaboration between fire engineers to define to the

thermal environment and structural engineers to determine the subsequent

structural behaviour.

References

1 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance

testing – Part II”. Fire Technology, 14(4), pp. 304-316, 1978.

2 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:

Method for Determination of the Fire Resistance of Elements of Construction:

BSI, 1987.

3 ISO 834-1. Fire-resistance tests — Elements of building construction — Part 1:

General requirements.

4 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings

Construction and Materials, 2000.

5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.

6 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.

7 Manzello, S. L., Grosshandler, W. L., Mizukami, T., “Furnace Testing of Full-

Scale Gypsum Steel Stud Non-Load Bearing Wall Assemblies: Results of Multi-

Laboratory Testing in Canada, Japan and USA”, Fire Technology, Vol. 46, 2010,

pp. 191-197.

Page 95: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

75

8 Thomas. P.H., “Modelling of compartment fires,” Fire Safety Journal, Vol. 5, 1983,

pp. 181 – 190.

9 Karlsson, B. and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.

10 Magnusson, S.E. and Thelandersson, S., “Temperature-time curves for the

complete process of fire development — a theoretical study of wood fuels in

enclosed spaces”, Acta Polytechnica Scandinavica, Stockholm, Vol. Ci 65, 1970.

11 Babrauskas, V. and Williamson, R.B., “Post-flashover compartment fires: Basis

of a theoretical model”, Fire and Materials, Vol. 2, 1978, pp. 39–53.

12 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel

Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,

1976.

13 Wickström, U., “Temperature calculation of insulated steel columns exposed to

natural fire”, Fire Safety Journal, Vol. 4, 1981, pp. 219-225.

14 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on

structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.

15 Lie, T.T., “Characteristic temperature curves for various fire severities”, Fire

Technology, Vol. 10, 1974, pp. 315-326.

16 Ma, Z. and Mäkeläinen, P., “Parametric temperature time curves of medium

compartment fires for structural design”, Fire Safety Journal, Vol. 34, 2000,

pp. 361-375.

17 Barnett, C.R., “BFD curve: a new empirical model for fire compartment

temperatures”, Fire Safety Journal, Vol. 37, 2002, pp. 437-463.

18 Franssen, J.M., “The Design Fire Tool OZone V2.0-Theoretical Description and

Validation on Experimental Fire Tests”, Civil and Structural Engineering

Department, University of Liege, Belgium, 2000.

19 Jeffers, A.E. and Sotelino, E.D., “Evaluating the Local Fire Response of Steel

Beams by Comparison to Fire Tests”, The 12th International Interflam Conference.

Nottingham, UK, 2010.

Page 96: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

76

20 Buchanan A., “The Challenges of Predicting Structural Performance in Fires”,

The 9th International Symposium on Fire Safety Science. Karlsruhe, Germany, 2008.

21 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and

Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th

International Symposium on Fire Safety Science, University of Maryland, USA,

2011.

22 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.

14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204

23 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of

the homogeneous temperature assumption in post-flashover compartment

fires”. Fire Safety Journal, 45, 2010, pp. 249-261.

http://www.era.lib.ed.ac.uk/handle/1842/3866

24 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern

Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra

Incêndio, Natal, Brazil, 2011.

25 Rein, G., Abecassis-Empis, G., and Carvel, R. Eds., The Dalmarnock Fire Tests:

Experiments and Modelling. School of Engineering and Electronics, University of

Edinburgh, 2007.

26 Lennon, T. and Moore, D., “The natural fire safety concept - full-scale tests at

Cardington”. Fire Safety Journal, Vol. 38, 2003, pp. 623 – 643.

27 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,

“Natural Fires in Large Scale Compartments”, British Steel, 1994.

28 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation

Openings – Comparison of Long and Wide Enclosures”. The 6th International

Symposium on Fire Safety Science, Poitiers, France, 1999.

29 Thomas, I., Moinuddin, K., and Bennetts, I., “Fire development in a deep

enclosure”. The 8th International Symposium on Fire Safety Science, Beijing, China,

2005.

Page 97: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

77

30 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,

Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the

World Trade Center Towers. NIST NCSTAR 1-5, 2005.

31 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,

Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire

Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST

NCSTAR 1-9, 2008.

32 Fletcher, I.A., Tall concrete buildings subject to vertically moving fires: A case study

approach. PhD thesis, School of Engineering, The University of Edinburgh, 2006.

http://www.era.lib.ed.ac.uk/handle/1842/3199

33 Zannoni, M. et al., “Brand bij Bouwkunde”, COT Instituut voor Veilingheids –

en Crisismanagement, December 2008.

34 Routley, J.G., “Interstate Bank Building Fire, Los Angeles, California”, U.S. Fire

Administration Technical Report 022.

35 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One

Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration

Technical Report 049.

36 Clifton, G.C., “Fire Models for Large Firecells”, HERA Report R4-83, 1996, with

proposed changes in HERA Steel Design and Construction Bulletin Issue No 54,

February 2000 and updates to referenced documents, September 2008.

37 Moss, P.J. and Clifton, G.C., “Modelling of the Cardington LBTF Steel Frame

Building Fire Tests”, 2nd International Workshop on Structures in Fire,

Christchurch, New Zealand, 2002.

38 Stern-Gottfried, J., Chapter 5 in: Travelling Fires for Structural Design, PhD Thesis,

School of Engineering, University of Edinburgh, 2011.

39 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and

Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th

International Interflam Conference, London, UK, 2007.

http://www.era.lib.ed.ac.uk/handle/1842/1980

Page 98: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

78

40 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach

to design fires for structural analysis of non-conventional buildings: A case

study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,

http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf

41 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel

Temperatures using Travelling Fires and Traditional Methods: Case Study for

the Informatics Forum Building”. The 12th International Interflam Conference.

Nottingham, UK, 2010.

42 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling

fires on a concrete frame”, Engineering Structures, Vol. 33, 2011, pp. 1635-1642.

doi:10.1016/j.engstruct.2011.01.034. Open access version at:

http://www.era.lib.ed.ac.uk/handle/1842/4907

43 Walton, W.D. and Thomas, P.H., "Estimating Temperatures in Compartment

Fires", Chapter 3-6 of the SFPE Handbook of Fire Protection Engineering, 3rd Edition,

2002.

44 Harmathy, T.Z., “A New Look at Compartment Fires, Part II”, Fire Technology,

Vol. 8, 1972, pp.326-351, doi:10.1007/BF02590537.

45 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire

Detectors”, Fire Technology, Vol. 8, 1972, pp. 181–195.

46 Bailey, C.G., Burgess, I.W., and Plank, R.J., “Analyses of the Effects of Cooling

and Fire Spread on Steel-framed Buildings”. Fire Safety Journal, Vol. 26, 1996,

pp. 273-293.

47 Ellobody E. and Bailey, C.G., “Structural performance of a post-tensioned

concrete floor during horizontally travelling fires”. Engineering Structures, Vol.

33, 2011, pp. 1908-1917.

48 Law, A., The Assessment and Response of Concrete Structures Subject to Fire. PhD

thesis, School of Engineering, The University of Edinburgh, 2010,

http://www.era.lib.ed.ac.uk/handle/1842/4574.

Page 99: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

79

49 Röben, C., Gillie, M., and Torero, J.L., “Structural behaviour of during a

vertically travelling fire”, Journal of Constructional Steel Research, Vol. 66, 2010,

pp. 191-197.

50 Flint, G., Fire Induced Collapse of Tall Buildings. PhD thesis, School of

Engineering, The University of Edinburgh, 2005,

http://www.era.lib.ed.ac.uk/handle/1842/1172.

51 Sandström, J., Cheng, X., Veljkovic, M., Wickström, U., and Heistermann, T.,

“Travelling Fires for CFD”, The 10th International Symposium on Fire Safety

Science, University of Maryland, USA, 2011.

52 Shestopal, V., Foley, M., Hewitt, J., Yii, E., and Bakker, F., “Spreading Fires in

FDS5 Modelling (Case Studies)” A Poster at The 12th International Interflam

Conference. Nottingham, UK, 2010.

Page 100: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

80

Page 101: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

81

4 The Influence of Travelling

Fires on a Concrete Frame

4.1 Introduction

Since the early 20th century, the Standard Fire test and associated temperature-time

curve [1, 2] have been used world-wide to give fire ratings to structural assemblies

and to design complete structures [3]. The Standard Fire temperature-time curve

was created in an attempt to regulate testing between different laboratories thereby

ensuring a uniform standard of safety. However, almost as soon as it was conceived,

a number of problems were identified with it. Notably, no account is taken of

differences in fuel load, fire compartment size or ventilation conditions, all of which

profoundly affect the behaviour of a compartment fire. To address some of these

shortcomings, other temperature-time curves have been proposed. Perhaps the most

widely known in structural design are the “parametric” fires curves. Initially

developed by Pettersson [4], these curves have been modified and are incorporated

Page 102: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

82

into the Eurocode structural design standards [5]. They allow design fires to be

calculated that, unlike the Standard Fire curve, depend on the fuel load, thermal

inertia of linings, and ventilation conditions of a fire compartment. Parametric fires

therefore predict more realistic temperature-time curves than the Standard Fire and

can be roughly replicated by burning wooden cribs in a small fire compartment.

Despite these benefits, parametric fires remain very crude representations of fires in

any but the simplest of compartments, as will be described in Section 4.2. Moreover,

they are unsuitable for application in the large, open-plan spaces that are a common

feature of many modern buildings. Thus, there remain significant shortcomings

amongst the traditional design methods for specifying the thermal inputs for use in

structural fire design, particularly for large compartments.

By contrast, over the past 20 – 30 years, knowledge and understanding of how

structures respond to elevated temperatures has developed rapidly and to a point

where it is now possible to include a large variety of phenomena in structural

models and to predict the response of structures subject to known temperature

loading with good accuracy [6, 7, 8]. Coupled with the recently developed

performance-based design codes [9, 10], these capabilities have given engineers the

freedom to design structures to resist high thermal loadings in innovative, efficient

ways.

Thus, while the ability to predict subsequent structural behaviour has reached an

advanced level, the thermal inputs used in structural fire design remain simplistic,

unchanged, and not representative of actual fire dynamics in large compartments.

The various limitations inherent in the traditional design methods mean that it is

difficult to justify continuing to develop and use complex structural models when

one of the dominating input parameters – thermal loading – remains very crudely

defined. Without some development of the method for specifying design fires, it

will be impossible to obtain the “consistent level of crudeness” which has been

identified as a need within the discipline [11]. In an attempt to rectify the mismatch

Page 103: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

83

in the levels of sophistication that are currently used for design fires and the

subsequent structural analysis, this paper adopts a new approach [12, 13, 14]. First, a

method of defining design fires that are sufficiently flexible to be applied to any fire

compartment is presented and discussed. The method has the key benefits of not

assuming a uniform temperature within a large fire compartment and allowing for

fires that travel within a compartment. Second, the paper considers the implications

of using these new design fires by applying them to the analysis of a concrete

framed structure subject to full-floor fires and comparing the predictions of various

measures of “structural distress” with those obtained when traditional fire curves

are used.

4.2 Limitations of Current Design Fires

Parametric and Standard Fires were validated by test data from small fire

compartments that were almost cubic. This test geometry allows for good mixing of

the fire gases and so is more likely to produce uniform temperature field within a

compartment. These conditions do not exist in real fires [15] and consequently

limitations must be placed on the form of compartment in which the traditional fire

curves may be used. For example, Eurocode 1 states that the parametric curves are

only valid for compartments with floor areas up to 500m2 and heights up to 4m, the

enclosure must also have no openings through the ceiling, and the compartment

linings are restricted to having a thermal inertia between 1000 and 2200J/m2s½K,

which means that highly conductive linings such as glass façades and highly

insulating materials cannot be taken into account. As a result, common features in

modern construction like large enclosures, high ceilings, atria, large open spaces,

multiple floors connected by voids, and glass façades are excluded from the range of

applicability of the current methodologies.

A recent survey of buildings in Edinburgh, UK [16], underlines the implications of

these limitations on the applicability of design fires, particularly for modern

Page 104: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

84

structures. For buildings built over a long period of time starting in the early 20th

century, 66% of their total volume falls within the limitations. However, in a newly

constructed, modern building that has open spaces and glass façades, only 8% of the

total volume is within the limitations. This suggests that modern building design is

increasingly producing buildings that contain compartments to which parametric

fires should not be applied.

Additionally, an assumption that has remained unquestioned with each

temperature-time curve no matter how they have been applied has been that of

uniform burning and uniform compartment temperature. It is assumed that every

part of a structural element or compartment is uniformly subject to the same

temperature – as defined by the temperature-time curve adopted. Although it may

be possible to replicate these conditions in a furnace, a recent experimental review

of post-flashover tests [15] has clearly demonstrated that temperature conditions are

non-uniform in most compartments. Moreover, major fires at the Windsor Tower

[17], World Trade Center [18, 19] and TU Delft [20] have shown that fires tend to

travel around large compartments rather than burn uniformly. Tests have also

shown the there is a high degree of temperature variation even within small

compartments [21, 22, 23].

Therefore, at present, designers are forced to either use parametric fires in

compartments for which they are not strictly applicable, apply unrealistic Standard

Fires to large compartments, or to resort to CFD models of fires in large

compartments that are labour intensive to produce. There is a clear need, then, to

address the limitations of the currently available design fires if modern

performance-based design is not to be restricted.

Page 105: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

85

4.3 Travelling Fires

In light of the various limitations outlined above, a new method for estimating

compartment fire temperatures based on the fundamental fire dynamics of the

compartment has been proposed [12, 23, 24]. This new method will be used

throughout this paper. It uses two temperature fields to represent the gas

temperature in a compartment: a high temperature in the flaming region of the fire

(the near field); and a cooler temperature for the rest of the compartment (the far

field). This approach provides a flexible technique whereby a large range of possible

fires in any compartment can be represented. For example, a fire which engulfs an

entire large floor plate simultaneously, as in traditional design methods, can be

represented, as well as a small fire that travels slowly from one end of a

compartment to the other. The full range can then be explored by parametrically

varying the size of the fire. This avoids the weakness of previous methods assuming

that arbitrary events lead to particular fire conditions, such as assuming that glazing

failure leads to one single temperature-time definition for an entire region. Instead,

consideration of a wide range of possible fire sizes covers for the inherent variable

nature of real fire events (outcome of the combination of a particular ignition

location, fuel distribution and ventilation conditions). Thus, a family of fires is

created ranging from a small travelling fire that burns for a long duration as it

travels, to a fire uniformly burning over the full extent of the floor for a shorter time

period. Therefore, the method addresses the two key shortcomings of existing

methods – restrictions on the nature of applicable fire compartments and the

assumption of uniform gas temperatures within a compartment – while still being

sufficiently concise for use in structural design.

4.3.1 Temperature Definition

The new design approach represents the horizontal temperature distribution of a

fire compartment by means of near field and far field regions, as illustrated in

Figure 4.1.

Page 106: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

86

(a) (b)

Figure 4.1: (a) Illustration of a travelling fire; (b) Near field and far field exposure

durations at an arbitrary point within the fire compartment.

The near field is the flaming region of the fire. Peak values in small fires have been

measured in the range of 800 to 1000°C [25] but temperatures of 1200°C have been

measured for larger enclosure fires [5]. This maximum value of 1200°C is chosen for

the near field to represent the worst case conditions. The far field represents the

temperature of the hot gases away from the flaming region. Far field temperatures

can be calculated using any engineering tool that gives temperature distributions

away from the fire, including hand calculations or computer modelling. For this

study, the simple ceiling jet correlation developed by Alpert has been used [26] and

is given in Eq. (4.1).

%�& − ∞ = 5.38�� )⁄ �+ ,⁄- (4.1)

where %�& is the maximum ceiling jet temperature(°C)

∞ is the ambient temperature (°C)

� is the heat release rate (kW)

) is the distance from the centre of the fire (m)

- is the floor to ceiling height (m)

Far field (Tff) Near field (Tnf)

Near field

travels over

time

Tnf

Tff

Initial

far field

heating

Posterior

far field

heating

T∞

Near field

heating

Gas

Te

mp

era

ture

After fire

cooling

time

Page 107: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

87

This correlation was developed for a stationary fire during steady state conditions

but is valid for travelling fires because the flame spread rate (~0.01m/s [5]) is much

lower than the velocity of the smoke (~1m/s). Thus, the far-field temperature

distribution in Eq. (4.1) moves with the fire in a quasi steady state form.

As the fire consumes the available fuel and ignites new material in its path, it moves

around the floor-plate. Consequently, the gas temperature adjacent to any given

structural element is constantly changing as the fire travels both near that element

and remote from it. To make the amount of information passed to a structural

analysis managable, the monotonically decreasing far field temperature distribution

from Alpert’s correlation is reduced to a single characteristic value, ��. To do this,

the far field temperature is taken as the fourth-power average of %�& (to favour

high temperatures in a bias towards radiation heat transfer and onerous structural

conditions) over the distance between the end of the near field, )/�, and the end of

the far field, )��. This average is calculated by Eq. (4.2).

�� = 01 2%�&345)677687 9: 4;

�)�� − )/��: 4; (4.2)

Figure 4.1 illustrates the concept of a near field and a far field for a travelling fire.

Any given location is exposed to the far field temperature for a period before the

arrival of the flaming, near field region. After all the fuel at the location has been

consumed and the near field moves away, it is then subjected to the far field

temperature again until all the fuel in the entire compartment has been consumed,

at which point the temperature returns to ambient and the structure cools.

4.3.2 Fire Size

The flexibility of the method stems from parametrically varying the size, shape, and

path of the fire. It is assumed that, once alight, any area of the floor plate will

Page 108: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

88

continue to burn at the same rate until all the fuel is consumed. The local burning

time for any fire size can, therefore, be simply calculated from the fuel load and the

heat release rate. Once the local fuel is burnt out, the fire will move to a new area.

After the fire has travelled around the whole compartment, the cooling of the

structure takes place. The fire size is varied, in this study from 1% to 100% of the

compartment floor area. Assumptions and details of how to calculate the resultant

heating from this method can be found in other papers by the authors [13, 14, 23].

4.4 Structural Failure Criteria

The methodology presented above can be used to study the impact of different

travelling fires on the response of a structure. However, without a means to

compare the structural response, it is impossible to draw any conclusions. There are

many different methods of assessment available for fire-affected structures of

varying degrees of complexity.

The simplest and most widely used measure of structural distress is maximum

deflection. Typically, failure is defined as a ratio of deflection, e.g. span/20 [2]. The

allowable deflection does not represent a value at which an assembly

catastrophically loses stability; rather, it is the maximum deflection allowable in a

furnace test in order to protect expensive experimental equipment. In spite of this,

deflection is a simple and useful measure which can be used to give some indication

of structural distress. It is possible to use the relative deflections caused by different

fires as a means for comparison.

Another simple measure of performance for concrete structures is the maximum

temperature of the tension reinforcement. Failure in steel members is often said to

have occurred when the axial capacity of a section is half its ambient capacity. For

reinforcing steel in concrete, this critical temperature is typically taken as 593°C [27].

Again, although this is a fairly arbitrary measure of “failure”, the temperature of the

Page 109: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

89

rebar offers a simple and easily comparable metric that can be used to examine the

relative impact of different fires on a structure.

The ultimate strain in the tension reinforcement is also often used as a definition of

failure; beyond this strain, the rebar can be assumed to have failed. This measure is

better suited to the numerical analysis of structures than to fire tests because of the

difficulties associated with instrumentation of rebar. However, the strain in the

tension steel provides another measure which can be used to compare the relative

impact of the different fires. The ultimate strain for steel at any temperature is

typically taken as 0.2 [10, 28].

4.5 Structural Modelling

The remainder of this paper is a case study that demonstrates how the above

travelling fire methodology and failure measures can be applied in a structural

analysis. Initially, a number of base case scenarios are considered and the

differences between the predicted structural responses compared; a parametric

study is then conducted to assess the validity and effect of the various assumptions

made by the new approach. Finally, the impact of the shape and path of the fire is

considered.

4.5.1 Structural Arrangement

The case study analyses the impact of travelling fires on a generic concrete office

building. The structure is a nine storey, flat-slab concrete frame, designed in

accordance with the Eurocodes [29, 30, 31]. A plan and elevation of the structure are

shown in Figure 4.2. The floor slabs are 200mm thick; the interior columns

400mm x 400mm; and the exterior columns 300mm x 300mm. The design strength of

the concrete in the columns is 48MPa, and that in the slabs 40MPa. In this paper fires

burning on the fourth floor are considered. This allows the structural effects of a

Page 110: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

90

mid-level fire to be analysed without the need to explicitly consider effects of the

foundations or the building’s top storey.

Figure 4.2: Plan and elevation of concrete structure, dimensions in metres.

Two finite-element models of the central floors of the structure were created using

the commercially available Abaqus [32] software. One was a heat-transfer model

developed to determine structural temperatures, the other a stress analysis model

produced to predict the mechanical response of the structure. The models were

sequentially coupled so the heat-transfer analysis results affected the mechanical

response. Both models extended from the base of the columns at the third-storey

level, to the top of the columns at the fifth-storey level. The floor slabs were

modelled using shell elements, the columns using three-dimensional solid elements

and the rebar using truss elements.

In the heat-transfer model, thermal properties were specified in accordance with

those of a 1.5% moisture content concrete, as defined in Eurocode 2 [9]. Heating of

the structure was analysed by applying relevant radiative and convective boundary

conditions to the surface of the structure. For the purposes of this study, an

Page 111: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

91

emissivity of 0.7 and a convective coefficient of 25W/m2K were assumed in

accordance with Eurocode guidance [9].

For the mechanical analysis, all of the material properties used in the model were

temperature dependent and in accordance with Eurocode 2 and the yield criterion

used for the concrete was the “damaged plasticity” model, based on the work of

Lubliner [33]. A series of mesh sensitivity studies were conducted to find the

optimum mesh density. The final mesh density used was 8 × 8 × 18 elements per

floor per column, and an average element size of 0.4735m in the slab.

The base of each column was assumed to be fixed in translation and rotation, and

the top of each column was fixed in all directions other than vertical. As the higher

storeys of the structure were not modelled, the equivalent loads that would have

been transferred into the column heads were calculated using a full-frame elastic

model and applied to the remaining structure during the loading phase of the

analysis. The central core of the building was not modelled explicitly but was

assumed to provide rigid support to the adjoining structure.

4.6 Base Case Fires

The base case family of fires were defined as fires that travelled linearly from one

side of the structure to the other, as shown in Figure 4.3. The fire sizes considered

were: 1%, 2.5%, 5%, 10%, 25%, 50% and 100% of the floor area. It was assumed that

the fuel load, $�, was 570MJ/m2 and the heat release rate per unit, � ", was

500kW/m2. The distance to the far field for Alpert’s equation was measured from the

centre of the fire at the mid-point of the building along the direction of fire travel, as

shown in Figure 4.4. This creates the shortest far field distance, which in turns leads

to the highest far field temperature possible for that specific scenario. This is done to

err on the side of conservatism. Figure 4.4 shows the distances to the end of the near

field and to the end of the far field for both the case where the near field is smaller

Page 112: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

92

than the core and the case where it is larger. The near field distance is simply

calculated from the geometry of the structure and the fire area for each case.

(a) (b)

Figure 4.3: (a) Progression of the 2.5% fire across the floor plate; (b) Progression of the 25%

fire across the floor plate. Bay numbers are indicated in both figures.

(a) (b)

Figure 4.4: The measurement of )�� and )/� for two different indicative fire sizes:

(a) small; and (b) large.

The fuel conditions above resulted in a local burning time of 19min for any single

area. For example, as there were four phases in the 25% fire size, it lasted for a total

burning duration of 76min, and had a far field temperature of 805°C. The near field

6

5

4

3

2

1

Far field

Far field

Near field

A

B

6

5

4

3

2

1

Far field

Far field

Near field

A

B

Near field

rnf

rff

Near field

rnf

rff

Page 113: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

93

temperature is taken as the flame temperature, assumed to be 1200°C [13]. The 2.5%

fire size, meanwhile, had a total burning duration of 760min and a far field

temperature of 325°C. Figure 4.5 shows the total burning duration and far field

temperatures for each of the base case fires. It should be noted for the 100% fire size,

the far field temperature is the same as the near field temperature.

Figure 4.5: Far field temperatures vs. total burning durations for different fire sizes.

Standard and two (“short hot” – EC1 100% and “long cool” – EC1 25%)

parametric Eurocode fire curves are also shown for reference.

4.6.1 Structural and Thermal Analysis

Thermal and structural analyses were conducted using the finite-element model

described above. To allow meaningful conclusions to be drawn from the modelling,

it should be noted that the analyses were intended to be comparative. Therefore, for

the remainder of this paper, the metrics that will be used to quantify the response of

the structure will be the three simple measures discussed above – temperature,

strain in the tension steel, and central deflection of each bay.

0

200

400

600

800

1000

1200

1400

0.1 1 10 100

Far

Fie

ld T

em

pe

ratu

re (°

C)

Time (hours)

1%

2.5%

5%

10%

25%

50%

100%

Std Fire

EC1 25%

EC1 100%

Page 114: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

94

Figure 4.3 shows the location of the near field part of the way through the 2.5% and

25% fire sizes. The heat transfer analyses allowed the temperature in the slab soffit

rebar to be monitored. Figure 4.6 shows the gas temperatures and corresponding

rebar temperatures for points A and B (indicated in Figure 4.3) during the 10% fire.

(a)

(b)

Figure 4.6: (a) Gas temperature and corresponding rebar temperature at point A; (b) Gas

temperature and corresponding rebar temperature at point B for a 10% linearly

travelling fire.

The influence of the near field on the rebar can be clearly seen as a temporary

increase in temperature. The prolonged exposure of point B to the far field prior to

the arrival of the near field causes the overall peak temperature to be higher than

that at point A. Figure 4.7a shows a similar plot of the temperature profiles for the

soffit rebar at the centre of bays 1 – 6 for the 5% fire size. It can be clearly seen that

the final bay to be subjected to the near field experienced the highest temperature;

the long pre-heat induced a higher maximum temperature in this bay which caused

it to be most critical by this metric. This trend was the same with each of the base

case fires.

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

Tem

pe

ratu

re (o

C)

Time (min)

Gas temperature

Rebar temperature

Point A

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

Tem

pe

ratu

re (o

C)

Time (min)

Gas temperature

Rebar temperature

Point B

Page 115: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

95

(a)

(b)

Figure 4.7: (a) Single point rebar temperature at the centre of bays 1 – 6 during the 5% base

case fire; (b) Average rebar temperatures for the whole of bays 1 – 6 for the 5%

base case fire.

Figure 4.7b shows the average temperature in the soffit rebar for each bay. Because

the near field of the 5% fire size does not cover the whole area of any bay

simultaneously, the average rebar temperatures are lower. The bay average rebar

temperatures are a more representative measure of structural vulnerability as they

will not be distorted by localized heating effects. For example, were a localized fire

to heat only a tiny area of the bay, it would have minimal impact on the overall

structural behaviour, but would induce high rebar temperatures. Thus, the bay

average rebar temperatures will be used as the measure of rebar temperature for the

remainder of this paper rather than point temperatures.

A comparison of the rebar temperatures induced in the final bay by the different

fires in the family is given in Figure 4.8 and shows clearly that the highest

0

100

200

300

400

500

600

0 100 200 300 400 500 600

Tem

pe

ratu

re (o

C)

Time (min)

Point 1Point 2Point 3Point 4Point 5Point 6

65432

1

0

100

200

300

400

500

0 100 200 300 400 500 600

Tem

pe

ratu

re (o

C)

Time (min)

Bay 1Bay 2Bay 3Bay 4Bay 5Bay 6

65432

1

Page 116: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

96

temperatures are caused by the medium duration fires: 10% and 25% fire sizes. For

the 2.5% fire the arrival of the near field at bay 6 is labelled, as is the end of the fire.

Figure 4.8: Temperature profiles for the average rebar in the final bay to be heated during

the base case fires.

A similar process was conducted for each of the structural measures. The absolute

value of each measurement technique can be normalised with respect to the

appropriate failure definition: 593°C for rebar temperature, span/20 for deflection,

and 0.2 for rebar strain. It is possible therefore to observe how the level of structural

distress varies with each curve in the family of fires. Figure 4.9 shows the trends for

each of the measures against fire size. As a comparison the structure was also

subjected to a Standard Fire, a “short hot” parametric fire and a “long cool”

parametric fire. The “short hot” fire had a peak temperature of 989°C and a total fire

time of 37min, and the “long cool” fire had a peak temperature of 915°C and a total

fire time of 145min. Both curves were generated by the parametric temperature-time

from Eurocode 1 [31] for the building being examined, varying the assumed glass

breakage in the façade for the ventilation factor. The short hot fire assumed 100%

glazing failure along the façade while the long cool fire assumed 25%.

0

100

200

300

400

500

0 200 400 600 800 1000 1200

Tem

pe

ratu

re (o

C)

Time (min)

2.5% Base

5% Base

10% Base

25% Base

50% Base

100% Base

Arrival of Near Field

End of Fire

Page 117: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

97

Figure 4.9: Change in structural distress with near field area: (top left) rebar temperature,

Standard Fire equivalent is 1h 37min; (top right) sagging tensile strain, value for

Standard Fire given after 3h; (bottom left) hogging tensile strain, Standard Fire

equivalent is 1h 18min; and (bottom right) deflection, Standard Fire equivalent

is 1h 54min.

The 25% fire size induced the highest degree of structural distress in each of the

failure metrics. The trend in every metric was the same: the medium sized fires (5%,

10% and 25%) caused a higher degree of structural distress than both the smaller

and the larger sized fires. It is also notable, that the temperature and deflection

measures show the structure as much closer to “failure” than the strain measures.

For each measure, a comparison with Standard and parametric fires is also made.

The parametric fires universally induced less extreme structural conditions than the

medium fire size base case scenario. The worst case travelling fire was equivalent to

1hr 37min of the of a Standard Fire in terms of rebar temperature, 1hr 18min for

hogging tensile stain and 1hr 54min for deflection. In contrast, the sagging strain

was less than that obtained during most of the base case and “long cool” fires; this

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0% 25% 50% 75% 100%

No

rma

lise

d T

em

pe

ratu

re

Fire Area

Rebar Temperature

Standard Fire

Parametric - Short Hot

Parametric - Long Cool0

0.01

0.02

0.03

0.04

0.05

0.06

0% 25% 50% 75% 100%

No

rma

lise

d S

tra

in

Fire Area

Sagging Strain

Standard Fire

Parametric - Short Hot

Parametric - Long Cool

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0% 25% 50% 75% 100%

No

rma

lise

d S

tra

in

Fire Area

Hogging Strain

Standard Fire

Parametric - Short Hot

Parametric - Long Cool0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0% 25% 50% 75% 100%

No

rma

lise

d D

efl

ect

ion

Fire Area

Deflection

Standard Fire

Parametric - Short Hot

Parametric - Long Cool

Page 118: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

98

was because there was no cooling phase during the Standard Fire so the structure

was not pulled into tension.

The results of the base case fires, and their comparison with the codified fires, have

shown that the traditional design methods do not necessarily produce the most

onerous case for the structure. Indeed a travelling fire based on fundamental fire

dynamics can induce a worse structural scenario. This is in agreement with previous

work for steel structures [12, 34]. It has been shown that the medium size (and

duration) fires induce the most extreme structural response; the short large fires and

the long small fires are less severe for the structure. Specifically the 25% area fire

produced the worst case for the structure. It has also been found that the lack of a

cooling phase in the Standard Fire does not allow all the forces that are likely to

develop over the course of a real fire to develop; it cannot, therefore be considered

conservative [35].

4.7 Parametric Study

A parametric study was conducted to establish the effect of the various assumptions

made in the travelling fire methodology on the predicted structural response. As the

25% fire was found to be the most severe by every metric for this structure, this fire

size was used throughout the parametric study.

4.7.1 Far Field Definition

First, the method used to define the far field temperature was varied, and the

response of the structure was monitored using the same metrics that were used in

the previous section. The cases studied are described below and illustrated in

Figure 4.10.

1. Single far field (base case). As with the previous analyses, Alpert’s far field

temperature profile was reduced to a single value by fourth power

averaging. The progress of the fire was assumed to move suddenly, i.e. it

Page 119: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

99

would jump from one quarter of the floor plate to the next after each burning

time. This assumption means the fire is in four specific locations (for the 25%

area fire) over the total burning duration.

2. Two far fields. Rather than reducing the far field to a single value for both

sides of the burning area, two separate far fields were assumed, one on

either side of the fire. Each far field had a unique temperature defined with

the fourth power average.

3. Alpert’s temperature profile (sudden). Rather than averaging the far field

temperature as above, the continuous temperature profile defined by

Alpert’s equation (Eq. 4.1) was directly applied to the structure. As with the

base case, the fire moved suddenly from area to area as the fuel was

consumed.

4. Alpert’s temperature profile (gradual). Alpert’s temperature profile was

used to define the far field, but the fire was assumed to progress gradually

across the structure, rather than jumping suddenly from one area to the next.

Figure 4.10: Example range of far field temperature definitions.

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40 45

Tem

pe

ratu

re (°

C)

Distance from End (m)

One Far Field

Two Far Fields

Resolved Far Field

Page 120: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

100

The results in Figure 4.11 show that there is little variation in the performance

metrics between the different approaches of defining the far field temperature. As

with the data in Figure 4.9 the results for each metric are normalised against the

relevant failure definition: 593°C for rebar temperature, span/20 for deflection, and

0.2 for rebar strain. Of the different proposed profiles, the “Alpert – sudden”

induced the greatest distress in terms of deflection (0.29m, normalised value of 0.84)

and hogging tension strain (0.03, normalised value of 0.19). However, these values

were only 0.5% and 3.6% in excess of the base case value, respectively. In terms of

rebar temperature, the base case had the highest value (450°C) by a marginal

amount (0.1% higher than the “two far fields” case) and the total variation between

the largest and smallest temperature was 10.6%. The largest value in terms of the

sagging tensile strain was obtained during the “Alpert – gradual” case (0.01). For

this profile, the maximum strain measured was 4.7% larger than the base case

equivalent.

Figure 4.11: The effect of far field temperature definition on each failure metric.

This study shows that the variations induced by the different fires in the most

critical structural measures are negligible. The variation in the less distressed

measures was slightly larger, but still remained small (<5%). It therefore appears

reasonable that the use of the simple, averaged, temperature profile, i.e. the base

0

0.25

0.5

0.75

1

Base case Alpert - Gradual Alpert - Sudden Two far fields

Norm

alised Faliure Criterion

Deflection Temperature Hogging strain Sagging strain

Page 121: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

101

case, for the whole of the far field temperature region provides appropriate results

and a higher level of detail is not needed. This makes the temperature definitions in

the heat transfer model significantly simpler to apply: a key consideration for the

use of such an approach in a design context.

4.7.2 Fire Shape and Path

The base case fire described above started at one end of the structure and then

progressed linearly across the floor-plate. A real fire could follow a number of

possible paths and it has long been recognised that to examine every possible fire

scenario would be unfeasible due to the large number of analyses required [3].

However, since the advent of modelling techniques such as the finite-element

method it has become possible to evaluate a number of different structural scenarios

quickly. This paper has developed a number of fires and applied them to the same

structure. In an attempt to quantify the impact that different fire paths and shapes

have on the structure, this study analyses the effect of three other possible fire

patterns with a fire size of 25% of the floor area. In addition to the linear base case,

the different fire shapes are illustrated in Figure 4.12 and are described below:

• Corner Fire. Initiated in one corner of the structure and spread around the

building’s core. Due to symmetry, results are the same for clockwise and

anti-clockwise fires.

• Ring Fire, Outwards. Initiated as a ring around the core, and spread

concentrically outwards.

• Ring Fire, Inwards. Initiated in a peripheral ring around the edge of the

structure, and spread concentrically inwards towards the core.

Page 122: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

102

Figure 4.12: Illustration of different fire shapes and paths.

The results were broadly similar with some metrics showing an increase and some

showing a decrease but there is some variation between the different fires paths.

The corner fire was found to be the most severe scenario. The relative increase in

comparison to the base case model was 8% for deflection (0.32m); 5% and 10% (0.04

and 0.01) for hogging and sagging strain respectively; and no change in the rebar

temperature. Figure 4.13 shows the difference between the four fire shapes

analysed. Therefore it can be concluded that the shape and path of the fire does

have a small impact on the response of the structure.

Figure 4.13: The influence of fire shape and path on the failure metrics.

1st burn region 2nd burn region 3rd burn region 4th burn region

Base case Corner Ring - InwardsRing - Outwards

0

0.25

0.5

0.75

1

Base case Ring - Inwards Ring - Outwards Corner

Norm

alised Faliure Criterion

Deflection Temperature Hogging strain Sagging strain

Page 123: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

103

4.8 Summary and Concluding Remarks

A comparative analysis of the impact of a number of different design fires on a

concrete frame has been conducted. A new approach to defining temperature-time

curves for design has been presented. The relative impact of the conventional

codified curves and the new travelling fire methodology has been studied.

The travelling fire approach is based on observations from real, large building fires,

and founded on the fundamental fire dynamics of a large open plan floor plate. It

allows a range of realistic fires to be considered and, thus, allows structural

engineers to better understand how different fires might affect the behaviour of a

building. Though based on complex temperature distribution data, a simplified

approach allows a single value far field temperature distribution. It has been

demonstrated that this simplification is a good approximation to more complex

temperature fields obtained from fundamental fire dynamics. The simplified far

field approach is easily implemented in finite-element codes.

The generic concrete frame which was subjected to the various fires was the same in

each of the analyses. It has thus been possible to draw strong comparative

conclusions, particularly given the variety of measures used to assess the structure,

which include:

• Travelling fires have a more severe impact on the performance of this

structure than the Eurocode parametric fires. The Eurocode fires cannot,

therefore, be considered conservative.

• The fires of medium duration and fire size are the most severe in terms of

their impact on the structure.

• The 25% fire size fire was conclusively found to be the most severe by every

measure used.

Page 124: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

104

• The assumption of a simplified far field temperature was valid: more

complex and realistic temperature profiles had little impact on the overall

structural behaviour.

References

1 ASTM E 119 - 00a Standard Test Methods for Fire Tests of Buildings

Construction and Materials, 2000.

2 BS476-20:1987. Fire Tests on Buildings Materials and Structures - Part 20:

Method for Determination of the Fire Resistance of Elements of Construction:

BSI, 1987.

3 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance

testing – Part II”. Fire Technology, Vol. 14, 1978, pp. 304-316.

4 Pettersson, O., Magnusson, S.E., and Thor, J., Fire Engineering Design of Steel

Structures, Publication 50. Stockholm: Swedish Institute of Steel Construction,

1976.

5 Drysdale, D., An Introduction to Fire Dynamics. John Wiley & Sons, 2nd Ed., 1998.

6 Franssen, J.M., Cooke, G.M.E., and Latham, D.J., “Numerical simulation of a full

scale fire test on a loaded steel framework”. Journal of Constructional Steel

Research Vol. 35, 1995, pg 377.

7 Bailey, C.G., Burgess, I.W., Plank, R.J., “Computer Simulation of a Full-Scale

Structural Fire Test”, The Structural Engineer Vol. 74, 1995, pg 93.

8 Gillie, M., Usmani, A.S., and Rotter, J.M., “A Sturctural Analysis of the

Cardington British Steel Corner Test”, Journal of Construction Steel Research”,

Vol. 58, 2002, pg. 427.

9 EN1992-1-2. Eurocode 2: Design of Concrete Structures - Part 1-2: General rules

- Structural fire design, 2004.

10 EN1993-1-2. Eurocode 3: Design of Steel Structures - Part 1-2: General rules -

Structural fire design, 2005.

Page 125: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

105

11 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,

The 9th International Symposium for Fire Safety Science, Karlsruhe, Germany, 2008.

12 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach

to design fires for structural analysis of non-conventional buildings: A case

study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,

http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf

13 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and

Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th

International Interflam Conference, London, UK, 2007.

http://www.era.lib.ed.ac.uk/handle/1842/1980

14 Stern-Gottfried, J., Rein, G., and Torero, J.L., “Travel Guide”, Fire Risk

Management, November 2009. pp. 12-16.

15 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of

the homogeneous temperature assumption in post-flashover compartment

fires”. Fire Safety Journal, 45, 2010, pp. 249-261.

http://www.era.lib.ed.ac.uk/handle/1842/3866

16 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.

14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204

17 Fletcher, I., Welch, S., Capote, J., Alvear, D., and Lázaro, M., “Model-based

analysis of a concrete building subjected to fire,” Advanced Research Workshop on

Fire Computer Modelling, Santander, Spain, 2007,

http://www.era.lib.ed.ac.uk/handle/1842/1988.

18 Gann, R.G., Hamins, A., McGratten, K.B., Mulholland, G.W., Nelson, H.E.,

Ohlemiller, T.J., Pitts, W.M. and Prasad, K.R., Reconstruction of the Fires in the

World Trade Center Towers. NIST NCSTAR 1-5, 2005.

19 McAllister, T.P., Gann, R.G., Averill, J.D., Gross, J.L., Grosshandler, W.L.,

Lawson, J.R., McGratten, K.B., Pitts, W.M., Prasad, K.R., and Sadek, F.H., Fire

Response and Probable Collapse Sequence of the World Trade Center Building 7. NIST

NCSTAR 1-9, 2008.

Page 126: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

106

20 Zannoni, M., Bos, G., Engel, K., and Rosenthal, U., Brand bij Bouwkunde. COT

Instituut voor Veilingheids – en Crisismanagement, 2008.

21 Abecassis-Empis, C., Reszka, P., Steinhaus, T., Cowlard, A., Biteau, H., Welch,

S., Rein, G., and Torero, J.L., “Characterisation of Dalmarnock fire test one,”

Experimental Thermal and Fluid Science, Vol. 32, pp. 1334 – 1343, 2008.

22 Welch, S., Jowsey, A., Deeny, S., Morgan, R., and Torero, J.L., “BRE large

compartment fire tests–characterising post-flashover fires for model

validation”. Fire Safety Journal, vol. 42, pp. 548 – 567, 2007.

23 Stern-Gottfried, J., Law, A., Rein, G., Gillie, M., and Torero, J.L., “A Performance

Based Methodology Using Travelling Fires for Structural Analysis”, The 8th

International Conference on Performance-Based Codes and Fire Safety Design Methods.

Lund, Sweden, 2010.

24 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G. “The Influence of Travelling

Fires on the Response of a Concrete Frame”, International Conference of Structures

in Fire. Lansing, Michigan, USA, 2010.

25 Audoin, L., Kolb, G., Torero, J.L., and Most, J.M.. “Average centreline

temperatures of a buoyant pool fire obtained by image processing of video

recordings”, Fire Safety Journal, Vol. 24, 1995, pp. 167-187. doi:10.1016/0379-

7112(95)00021-K.

26 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire

Detectors”, Fire Technology, Vol. 8, 1972, pp. 181–195.

27 Kodur, V.K.R. and Harmathy, T.Z., “Properties of Building Materials”, SFPE

Handbook of Fire Protection Engineering. 2008.

28 CEB-FIB. Fire Design of Concrete Structures: Structural Behaviour and

Assessment. Lausanne: FiB, 2008.

29 EN1992-1-1. Eurocode 2: Design of Concrete Structures - Part 1-1: General rules

and rules for buildings, 1999.

30 EN1992-1-2. Design of Concrete Structures - Part1-2: General rules- Structural

fire design, 1992.

Page 127: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

107

31 EN1991-1-2. Eurocode 1: Actions of Structures - Part 1-2: General Actions -

Actions on Structures Exposed to Fire, 1999.

32 ABAQUS. ABAQUS Analysis User's Manual. Providence: Dassault Systemes

Simulia Corp, 2008.

33 Lubliner, J., Oliver, J., Oller, S., and Onate, E., “A Plastic-Damage Model for

Concrete”, International Journal of Solids and Structures Vol. 25, 1989 pg. 299.

34 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel

Temperatures using Travelling Fires and Traditional Methods: Case Study for

the Informatics Forum Building”. The 12th International Interflam Conference.

Nottingham, UK, 2010.

35 Röben, C., The effect of cooling and non-uniform fires on structural behaviour. PhD

thesis, School of Engineering, The University of Edinburgh, 2006.

Page 128: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

108

Page 129: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

109

5 Refinement and

Application of the Travelling

Fires Methodology

5.1 Introduction

Close inspection of accidental fires in large, open-plan compartments reveals that

they do not burn simultaneously throughout an entire enclosure. Instead, these fires

tend to move across floor plates as flames spread, burning over a limited area at any

one time. These fires have been labelled “travelling fires”.

Despite these observations, fire scenarios currently used for the structural fire

design of modern buildings are based on one of two traditional methods for

specifying the thermal environment; the standard temperature-time curve (which

has its origins in the late 19th century [1]) or parametric temperature-time curves,

Page 130: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

110

such as that specified in Eurocode 1 [2]. These methods assume uniform burning

and homogeneous temperature conditions throughout a compartment, regardless of

its size. These two assumptions, which have never been confirmed experimentally,

lead to limitations in the use of the traditional methods in large compartments.

Details of the limitations and their implications are given in the literature [3, 4, 5].

Accidental fires that have led to structural failure [6, 7, 8, 9] have been observed to

travel across floor plates, and vertically between floors, rather than burn uniformly.

Travelling fires have also been observed experimentally in compartments with non-

uniform ventilation [10, 11, 12].

Even though the traditional methods have inherent assumptions of fire behaviour

different from that observed in accidental and experimental fires, in the past they

were generally deemed to be conservative, and therefore appropriate for

engineering design. However, recently travelling fires have been shown to be more

challenging to structures than the design fires from traditional methods [4, 13].

Moreover, recent advances in structural analysis and modelling techniques are

aimed at determining the true performance of a building exposed to fire. Therefore,

there is a need for a more realistic definition of fire scenarios to obtain a more

accurate characterisation of building performance. Because current engineering

analysis of the structural response often involves the use of sophisticated computer

modelling, it is also important to ensure a consistent level of crudeness across the

whole analysis [14, 15].

To address this need, a methodology that utilises physically-based fire dynamics for

large enclosures, based on travelling fires, has been developed. It has been

formulated to enable collaboration between fire safety engineers to define the fire

environment and structural fire engineers to assess the subsequent structural

behaviour, which is an identified need within the structural fire community [14, 15].

Page 131: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

111

This paper presents the general framework and analytical details of this travelling

fires methodology, which produces temperature fields for a range of fire sizes.

These results are used to calculate the heating of a generic concrete structure. A

sensitivity study is conducted to determine the relative impact of the methodology’s

numerical, physical and building parameters on the structure.

5.2 Travelling Fires Framework

The goal of the methodology developed in this paper is to calculate the fire-induced

thermal field such that it is physically-based, compatible with the subsequent

structural analysis, and accounts for the fire dynamics relevant to the specific

building being studied. In order to achieve this, a fire model must be selected that

provides the spatial and temporal evolution of the temperature field. This model is

then applied to the particular compartment of interest.

The fire-induced thermal field is divided in two regions: the near field and the far

field. These regions are relative to the fire, which travels within the compartment,

and, therefore, move with it. The near field is the burning region of the fire and

where structural elements are exposed directly to flames and experience the most

intense heating. The far field is the region remote from the flames where structural

elements are exposed to hot combustion gases (the smoke layer) but experience less

intense heating than from the flames. The near and far fields are illustrated in Figure

5.1.

Because the initiation and end of the fire results in a very fast rise and decrease in

gas temperature relative to the structural heating, these phases can be assumed to be

instantaneous for the temperature field (see Figure 5.8 for a fast return to ambient).

This is because the larger an enclosure is, the lower the importance of the thermal

inertial of its linings, thus the faster the growth and decay phases will be. In other

words, the transport of the hot gases in the smoke layer is faster than the heat

Page 132: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

112

transfer to the surfaces. Note that the cooling of the structure is not neglected; only

the brief decay phase of the fire environment is shortened.

(a) (b)

Figure 5.1: (a) Illustration of a travelling fire; (b) Near field and far field exposure

durations at an arbitrary point within the fire compartment.

For most large compartments, travelling fires are likely to be fuel bed controlled. In

fact, a recent review by Majdalani and Torero [16] of early CIB tests and the

resulting analyses of compartment fire behaviour done by Philip Thomas and others

highlights that ventilation controlled fires are unlikely in large enclosures and that

they are not necessarily more conservative for structural analysis than fuel bed

controlled fires. Majdalani and Torero note that while the different burning

behaviour between ventilation and fuel bed controlled fires was clearly stated in the

original studies, ventilation controlled fires have nonetheless been assumed to be

the most severe case for design. Therefore traditional methods of calculating the

burning rate, based on correlations for ventilation limited fires in relatively small

compartments, are inappropriate for use with travelling fires.

The methodology does not assume a single, fixed fire scenario but rather accounts

for a whole family of possible fires, ranging from small fires travelling across the

floor plate for long durations with mostly low temperatures to large fires burning

for short durations with high temperatures. Temperature-time curves for a family of

fires are shown in Figure 5.2. Using the family of fires enables the methodology to

Far field (Tff) Near field (Tnf)

Near field

travels over

time

TimeG

as

Tem

pe

ratu

re

Near Field

Initial

Far Field

Heating

Posterior

Far Field

Heating

Post Fire

Cooling

Tnf

T∞ ttotaltb

Page 133: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

113

overcome the fact that the exact size of an accidental fire cannot be determined a

priori. This range of fires allows identification of the most challenging heating

scenarios for the structure to be used as input to the subsequent structural analysis.

Figure 5.2: Temperature-time curves on a log x-axis for a family of fires at the final location

along the fire path. Cooling to ambient temperature starts after the last point in

each curve.

Each fire in the family burns over a specific surface area, denoted as ��, which is a

percentage of the total floor area, �, of the building, ranging from 1% to 100%.

Compared to this approach, the conventional methods only consider full size fires,

which are analogous to the 100% fire size in this methodology. All other burning

areas represent travelling fires of different sizes which are not considered in the

conventional methods.

The methodology is independent of the fire model selected and can utilise simple

analytical expressions or sophisticated numerical simulations. The first version of

this methodology used the Computational Fluid Dynamics (CFD) code Fire

0

200

400

600

800

1000

1200

1400

0.01 0.1 1 10 100

Ga

s Te

mp

era

ture

(oC

)

Time (hours)

1.25%

5%

10%

25%

50%

100%

Page 134: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

114

Dynamics Simulator (FDS) as the fire model [17]. Later work was developed using

an analytical correlation [4, 13, 18]. The work in this paper is developed further from

the earlier analytical work of Law et al. [4]. Details of each step of the methodology

are given in the following section.

5.3 Analytical Model

The analytical correlation used, in lieu of CFD modelling, was selected for several

reasons. The analytical model is simple and easy to use, while still providing the

correct dynamics (see Section 5.3.2). It also provides a consistent level of crudeness

with the heat transfer calculations performed to assess structural performance. And

it does not have the high computational cost of CFD (which is on the order of days

to calculate one fire scenario) associated with it and, therefore, enables consideration

of many more scenarios and sensitivity studies than would have been practical with

CFD models.

It is noted, however, that the correlation used is a simplification of the actual fire

dynamics of the cases being examined and is only applicable to a limited set of

scenarios where it is valid, such as a single floor without interconnection to other

levels. However, given the benefits of the points listed above, the analytical

correlation was deemed sufficient to progress development of the methodology.

The following sections present the details needed to calculate the temperature field

for the family of fires, using the analytical correlation selected.

5.3.1 Burning Times

As the exact size of a potential fire in a building cannot be determined a priori, and

the calculation methods for burning rates are inappropriate for large compartments,

this methodology assumes the heat release rate of a fire by considering a wide range

of possible sizes. It is assumed that there is a uniform fuel load across the fire path

Page 135: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

115

and that the fire will burn at a constant heat release per unit area typical of the

building load under study. From this, the total heat release rate is calculated by Eq.

(5.1).

� = ��� " (5.1)

where � is the total heat release of the fire (kW)

�� is the floor area of the fire (m2)

� " is the heat release rate per unit area (kW/m2)

The local burning time of the fire over area, ��, is calculated by Eq. (5.2).

"# = $�� " (5.2)

where "# is the burning time (s)

$� is the fuel load density (MJ/m2)

For the case study presented below, the fuel load density, $�, is assumed to be

570MJ/m2, as per the 80th percentile design value [19] for office buildings. The heat

release rate per unit area, � ", is taken as 500kW/m2 which is deemed to be a typical

value for densely furnished spaces, as design guidance [20] gives this value for retail

spaces. Based on these two values, the characteristic burning time, "#, is calculated

by Eq. (5.2) to be 19min. This time correlates well to the free-burning fire duration of

domestic furniture, which Walton and Thomas [21] note is about 20min. It is also in

line with Harmathy’s [22] observation that a fully developed, well ventilated fire

will normally last less than 30min.

Note that the burning time is independent of the burning area. Thus the 100%

burning area and the 1% burning area will both consume all of the fuel over the

specified area in the same time, "#. However, a travelling fire moves from one

Page 136: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

116

burning area to the next so that the total burning duration, "EFE�G, across the floor

plate is extended (see Eq. (5.9) in Section 5.3.3). This means that there is a longer

total burning duration for smaller burning areas.

The total burning duration for a single fire size can reach a theoretical maximum,

denoted as "EFE�G∗ , which is equal to the local burning time multiplied by the ratio of

floor area to the fire size, plus one additional local burning time. For example, a 25%

fire has a ratio of floor area to fire area of four, so adding one local burning time to

this gives five times the local burning time, or 95min, for the total burning duration.

Similarly, the maximum total burning duration for a 1% fire is 1919min. For full

details of the derivation of "EFE�G∗ , see Eq. (5.10) in Section 5.3.3.

5.3.2 Near Field vs. Far Field

The near field is dominated by the presence of flames. The maximum possible

structural heating would result from direct contact of the flames and a structural

element. Hence it is assumed that there is direct contact and peak flame

temperatures are used in this methodology. These temperatures have been

measured in small fires in the range of 800 to 1000°C [23] and up to 1200°C in larger

fires [24]. The maximum value of 1200°C is chosen here for the near field

temperature to represent worst case conditions. A sensitivity study on the effect of

this parameter value over the experimental range of peak flame temperatures is

presented in Section 5.5.7.

The far field temperature decreases with distance from the fire. The maximum

exposure to hot gases results when the structural element is on the exposed side of

the ceiling. Therefore temperatures at the ceiling are used in this methodology. An

analytical expression capturing the decrease of temperature with distance as a

function of the fire heat release rate would take the general form given in Eq. (5.3).

Page 137: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

117

��2I3 = J� KLIMN (5.3)

where �� is the far field temperature (°C)

� K is the convective heat release rate (W)

J is a constant parameter related to geometry and physical properties (-)

I is the horizontal distance from the fire (m)

O is the power law coefficient for heat release rate (-)

P is the power law coefficient for distance (-)

The decrease with distance is due to the incremental mixing of hot gases with fresh

air as they flow away from the fire source. This is a similar mixing process that takes

places in a vertical turbulent fire plume. The scale analysis of an inert mixing plume

[24, 25] gives α of 2/3 and β of 5/3.

The experimental and theoretical work by Alpert [26] provides the full expression

and the coefficients valid for an axi-symmetric, unconfined ceiling jet as a function

of radial distance from the fire centre. The correlation is given below in Eq. (5.4).

Alpert found experimentally that α and β are both 2/3, and that there is a

dependence on the inverse of the ceiling height (thus yielding a combined power

law coefficient for the spatial distance of 5/3 as predicted by the scale analysis).

%�& − ∞ = 5.38�� )⁄ �+ ,⁄- (5.4)

where %�& is the maximum ceiling jet temperature(°C)

∞ is the ambient temperature (°C)

� is the total heat release rate (kW)

) is the distance from the centre of the fire (m)

- is the floor to ceiling height (m)

Page 138: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

118

The Alpert correlation uses the total heat release rate, rather than its convective

portion which is related to buoyancy. This is due to the fact that the heat release

rates of pool fires, which were the basis of the correlation, are often reported as total

values and not convective [27]. The specific pool fires used for the development of

the Alpert correlations were alcohol pool fires, in which the radiative fraction is

negligible. Therefore, for application in this methodology, the heat release rate is

assumed to be purely convective, i.e. the radiative fraction is taken to be zero.

Alpert gives a piecewise equation for maximum ceiling jet temperatures to describe

the near field (r/H ≤ 0.18) and far field (r/H > 0.18) temperatures. But only the far

field equation is used here. The methodology assumes the near field to be the flame

temperature and does not use the expression given by Alpert. If the results of Eq.

(5.4) exceed the specified near field temperature at any point, they are capped at the

flame temperature.

This correlation was used in previous work of this methodology [4, 13, 18]. Its use

for horizontally travelling fires requires the further assumption that the coefficient,

J, does not change significantly when the linear distance, I, replaces the radial

distance, ), given by Alpert (planar vs. axi-symmetrical configurations). Therefore,

the linear distance, I, is used in the methodology.

It is also noted that the correlation assumes an unconfined ceiling with no

accumulated smoke layer. However, these strict limitations are ignored in the

application to this methodology. This has been done as it is a simple correlation and

was chosen to provide an approximate and straightforward calculation of the

temperature field that is sufficient to progress the development of the methodology.

Further sophistication and accuracy could be added to this framework as needed.

As a point of comparison between the axi-symmetric ceiling jet correlation and a

planar case, a set of CFD simulations were run using FDS v5.5.3. The simulations

examined the temperature decrease with linear distance from a 147MW fire (the

Page 139: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

119

25% fire size examined in Section 5.5) over a 28m wide strip located at one end of a

large compartment 42m long by 28m wide and 3.6m high (see Section 5.4 for

details). A grid sensitivity study was conducted to ensure good resolution and the

final cell size was set at 40cm. Three cases were investigated: 100% ventilation

opening (the whole façade is open), 50% ventilation opening, and 25% ventilation

opening. While very different ventilation scenarios were investigated, Figure 5.3

shows that the ceiling jet correlation provides a similar decay with distance (similar

P value) to the FDS models. The temperature agreement is better at larger distances.

Figure 5.3: Comparison of Alpert’s ceiling jet correlation with three FDS models of varying

ventilation for a 147MW, 28m wide fire (25% fire size) burning at one end of the

compartment (see Section 5.4 for details).

The values of P for the three FDS curves are 0.605 for 100% ventilation, 0.502 for

50% ventilation, and 0.463 for 25% ventilation. These values are similar to the 2/3 P

value from Alpert’s correlation. The modelling results provide confidence that the

ceiling jet correlation, while not exactly capturing the fire dynamics of each scenario

of interest here, gives appropriate and conservative results.

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35 40 45

Tem

pe

ratu

re (o

C)

Distance (m)

Alpert Correlation

FDS - 100% Ventilation

FDS - 50% Ventilation

FDS - 25% Ventilation

Near Field Far Field

Page 140: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

120

The previous work of this methodology [4, 13, 17, 18] took a single representative

temperature for the far field for each fire size, independent of distance. The work in

this paper, however, relaxes this simplification and allows for spatially varying far

field temperatures to be carried into the heating calculations. While this creates

more information to pass to the structural analysis, it provides a more accurate

representation of the fire dynamics for each scenario, which may be particularly

important for analyses of whole frame behaviour.

5.3.3 Spatial Discretisation

It is assumed that the fire extends the whole width of the building and travels in a

linear path along the structure’s length. Other fire paths are possible but results

shown in [4] demonstrate that they do not greatly alter the structural response. Thus

a single linear path is chosen for this further development of the methodology. As

the far field temperature is assumed uniform along the width of the building but

varies along its length for the assumed linear path, the problem is treated as one-

dimensional. Thus the far field temperature for any given fire size can be calculated

at any position in the structure by its linear distance from the fire. This discretisation

is similar to the strips examined by Clifton in his Large Firecell Model [28].

The fire is assumed to travel at a constant spread rate, Q, across the floor plate. This

is calculated by Eq. (5.5) and is related to burning time and fire size.

Q = R�"# (5.5)

where Q is the spread rate (m/s)

R� is the length of the fire (m)

Given that there is a fixed local burning time (based on the assumption of a uniform

fuel load density and a constant heat release rate per unit area, as explained in

Section 5.3.1), there is a one-to-one relationship between fire size and spread rate.

Page 141: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

121

This corresponds with the logic that the bigger the fire, the faster it moves. For

example, a fire that is 50% of the floor area (R� = 0.5R) would have a spread rate five

times faster than a 10% fire (R� = 0.1R3, as the local burning time is the same for

both.

To track the fire location over time and enable calculation of the far field

temperature at various distances, the building is broken up into numerous nodes,

each with a fixed width ∆I (also referred to as the grid size). Each node has a single

far field temperature at any given time. Therefore the more elements that are used,

the better resolved the far field temperature is (see Section 5.5.2). As the fire travels

across the floor plate, nodes go from being unburnt, to on fire, to burnt out.

Figure 5.4 illustrates the one-dimensional discretisation of the building showing the

grid size (∆I), total length (R), fire length (R�), far field distance (I��), node

references, and the leading and trailing edges of the fire. The near field distance is

half the fire length, while the far field distance (I��) is taken from the fire centre to

the node being examined (node S).

Figure 5.4: Illustration of spatial discretisation, showing the nodes of grid size, ∆I, and the

characteristic lengths of the problem. The fire (orange) travels at spread rate, Q,

towards the unburnt nodes (white), leaving burnt-out nodes (grey) behind.

Δx Lfs

Node 1 Node iNode 2 Node 3 Node 4

xffxi

Node i + 1 Node nNode n - 1Node i - 1

L

Node 5

Trailing Edge Leading Edge

Page 142: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

122

Each node can be described by its index, varying from 1 to n. The distance, Ib, from

a fixed reference point, taken here as the left end of the structure where the fire is

assumed to start, to another point can be described by Eq. (5.6).

Ib = 2S − 0.53∆I (5.6)

where Ib is the position relative to the end of the structure (m)

S is the node reference (-)

∆I is the grid size (m), also given by R �⁄

The relative positions of the fire location and the node can be tracked over time to

give a full transient evolution of the temperature field, including the passage of the

near and far fields (see Figure 5.1b and Figure 5.2). In order to adequately resolve

the movement of the fire, the time step, ∆"∗, is determined by Eq. (5.7).

∆"∗ = ∆IQ (5.7)

This definition allows the time step to capture the movement of the fire from one

node to the next. If the time step is longer than that calculated by Eq. (5.7), then

important information is lost. However, note that there is no benefit in making a

smaller time step. This is because a node cannot be partially occupied by the fire,

and thus each node has only one temperature for each time step. A finer time step

would yield consecutive times with the same temperature. Therefore the time step

in this work is always set by Eq. (5.7).

The time the fire spends at one node location, "b, is the sum of the travel time across

the node plus one local burning time. The whole node is assumed to start burning

when the leading edge of the fire enters from the near side. Then the whole node is

burnt out when the trailing edge of the fire passes the far side. This is given by Eq.

(5.8).

Page 143: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

123

"b = ∆IQ + "# (5.8)

As the fire travels across � − 1 nodes (the initial condition has node 1 burning at

" = 0), the total burning duration, "EFE�G, is the travel time across the rest of the floor

plate plus one burning time. This fact, plus noting that � = R ∆I⁄ , means the total

burning duration is given by Eq. (5.9).

"EFE�G = "# cR − ∆IR� + 1d (5.9)

As can be seen from Eq. (5.9), the total burning duration is a multiple of the local

burning time. This multiple of the local burning time is greater for smaller fire sizes,

meaning longer total burning durations. This explains why travelling fires account

for the longest burning fires that can take place in a large compartment and, indeed,

corresponds well to those observed in accidental fires [3].

Note that the total burning time also depends on the grid size (due to the initial

condition). The largest grid size that can be used to ensure that a given fire size is

fully resolved is ∆I = R�. A larger grid size would lead to the fire only occupying a

portion of any node, which is inconsistent with the assumptions of this

methodology. Placing this maximum grid size in Eq. (5.9), gives a total burning time

of "EFE�G = "#�R R�⁄ �. For example, the total burning duration for a 25% fire is 76min,

which is four times the local burning time (19min). The approach taken in earlier

work [4, 13, 18] used the largest grid size only and therefore had total burning

durations along these lines. However, as the grid size is reduced, the total burning

duration increases. The longest possible total burning duration, denoted as "EFE�G∗ , is

the limit of "EFE�G as the grid size approaches zero (the smallest possible grid size), as

given in Eq. (5.10).

"EFE�G∗ = lim∆&→g "EFE�G = "# c RR� + 1d (5.10)

Page 144: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

124

This means that the total burning duration is up to one local burning time longer

with a fine grid resolution than with a coarse one. For the same 25% fire size

example, the total burning duration with a very well resolved grid would approach

five times the local burning time, or 95min. This additional burning time, which was

not considered in previous versions of the methodology, represents the time period

of initial fire growth before the fire reaches its full size and the final stages of the fire

as it burns out and is again smaller than its full size. This is not accounted for in the

coarse grid case, which assumes the fire initialises and burns out at its peak size.

5.4 Application to a Generic Structure

The travelling fires methodology presented here is applied here to a case study of a

generic concrete frame, shown in Figure 5.5. The structure is based on that used in

Law et al. [4], but without the central core. The compartment is 42m long, 28m wide

and 3.6m high. There are six structural bays along the length of the building, and

four across its width. Each bay is 7m x 7m. The fire is assumed to ignite at one end

of the structure, occupy the full width and burn along its length over time as

illustrated in Figure 5.5.

A family of fires was investigated with sizes ranging from 1% to 100% of the floor

plate. A selection of fires is given in Table 5.1, showing the fire size and area, the

heat release rate calculated from Eq. (5.1), the maximum total burning duration

from Eq. (5.10), and the spread rate from Eq. (5.5).

Page 145: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

125

Figure 5.5: The generic concrete structure used for the case study.

Fire size hi (m2) j (MW) kklk�m∗ (min) n (m/min) 1% 11.8 5.9 1919 0.02

2.5% 29.4 14.7 779 0.06

5% 58.8 29.4 399 0.11

10% 117.6 58.8 209 0.22

25% 294 147 95 0.55

50% 588 294 57 1.1

75% 882 441 44.3 1.7

100% 1176 588 38 2.2

Table 5.1: A selection from the family of fires.

The burning durations of the larger fire sizes are of the same order of magnitude as

those predicted by the traditional methods [2]. The smaller fire sizes have burning

durations on the order of those observed in large, accidental fires [7, 8, 9]. For

example, the One Meridian Plaza fire in Philadelphia in 1991, which had horizontal

and vertical flame spread, lasted for almost 19 hours [29]. The range of spread rates

from the family of fires also corresponds well with physical values. Quintiere [30]

gives the rough order of magnitude of lateral fire spread on thick solids as 0.1cm/s

28m

654321

Far field

(not yet burnt)

Far field

(burnt out)

Near field

(fire)

Travel Direction

Bay References

Column

42m

Ignition at this side

Page 146: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

126

(0.06m/min) and of “forest and urban fire spread” between 1 and 100cm/s (0.6 to

60m/min). This again highlights the advantage of considering a range of fire sizes in

this methodology, as the burning duration and spread rate of an accidental fire

cannot be calculated a priori.

The family of fires created was used to generate transient gas phase temperature

fields across the structure. The temperature fields were then used as input to

calculate the resulting in-depth concrete temperature at the rebar location as a

simple measure of structural performance. The hotter the rebar temperature, the

poorer the structural performance is deemed to be. One-dimensional conductive

heat transfer inside the material was considered with boundary conditions for

convective and radiant heating from the gas phase as well as reradiation. The heat

transfer was solved by means of finite differences, as detailed in Appendix A. Law

et al. [4] showed that the average rebar temperature across a bay is a more critical

parameter for the structural response than that of a single point. Therefore to obtain

the bay average rebar temperatures (referred to as the bay temperature), the average

across the whole bay is calculated from results of the one-dimensional, in-depth

heat transfer method at each node.

An alternative to this approach would be to use a three-dimensional heat transfer

method and then calculate the full structural response by use of a detailed Finite

Element Model (FEM). This was the approach taken in the work done by Law et al.

[4]. For comparison, the bay average temperature results of the method used in this

paper were found to be between 7 to 15% higher than that calculated by Law et al.

Therefore this method is deemed appropriate, especially considering the differences

in comparison to a FEM approach (one vs. three-dimensional heat transfer, constant

vs. temperature dependent concrete properties, and varying heat transfer

formulations). The simple approach used here allows for rapid calculation of a large

variety of parameters which would be computationally restrictive to do with full

FEM analyses.

Page 147: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

127

5.5 Parameter Sensitivity Study

One aim of this methodology is to allow fire safety engineers to interface with

structural fire engineers to determine the most appropriate design fire scenarios

prior to the detailed structural analysis. It is the intent of this sensitivity study to

highlight the important parameters that should be considered in design.

The parameter values for the base case scenario and the ranges investigated are

given in Table 5.2. Unless specified otherwise, the base case values are used. The

study includes building, physical, and numerical parameters. Building parameters

are the actual quantities related to the building structure and its contents. Changes

in these parameters come from differing building designs or uses. Physical

parameters are those related to the temperature field and heat transfer mechanisms.

Numerical parameters are those required to generate the temperature fields and

heating but without physical meaning, such as the grid size. These last two sets of

parameters do not depend on the building design or its use, but on the theoretical or

numerical aspects of the methodology. As the fire size is the fundamental input

variable to the methodology, it is not classified as a parameter but a variable.

The following sections present the sensitivity of each of the parameters in Table 5.2.

5.5.1 Fire Size

Figure 5.6a shows the variation of peak rebar temperature with fire size ranging

from 1.25% to 100% for a grid size of 0.2625m. This grid size was selected as it

divides evenly amongst a large number of fire sizes.

Page 148: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

128

Parameter Range Base Case Parameter

Type Comment

Fire Size

(��)

1% – 100% of

floor plate 10%

Main

variable

Range is parametrically generated to

cover all possibilities. Base case value

determined by analysis in Section 5.5.1.

Grid Size

(∆I) 0.21 – 42m 1.05m Numerical

Range is to have a well resolved grid for

the smallest fire (1%) to the coarsest

possible for the largest fire (100%). Base

case value determined by analysis in

Section 5.5.2.

Rebar Depth

(56) 20 – 50mm 42mm Building

Range taken to be representative of

typical range in real buildings. Base case

value as per the design of the case study

building [4].

Bay Location 1st – 6th bay 6th bay Building

Range is all six bays of the structure. Base

case value selected as it is the most

onerous for the structure as shown in

Section 5.5.4.

Bay Size

(R#) 1.05 – 21m 7m Building

Range is from the bay being the base case

grid size (1.05m) to half the structure’s

length (21m). Base case value as per the

design of the case study building [4].

Fuel Load

Density

($�)

285 –

1500MJ/m2 570MJ/m2 Building

Range covers sparsely furnished

(classroom) to densely loaded (library)

spaces. Base case value is taken as the 80th

percentile design value [19] for office

buildings.

HRR per Unit

Area

(� ") 200 –

800kW/m2 500kW/m2 Building

Range taken for representative values of

real fuels in non-industrial buildings [31].

Base case value is taken as densely

furnished office [20].

Emissivity

(o) 0.2 – 1 0.7 Physical

Range taken to test sensitivity; however

values in an accidental fire are expected

to be above 0.5. Base case value is taken

from Eurocode guidance [2].

Convective

Coefficient

(ℎK)

10 –

100W/m2 K 35W/m2 K Physical

Range taken to represent bounds in a fire

condition [32]. Base case value is taken

from Eurocode guidance [2].

Near Field

Temperature

(/�)

800 – 1200°C 1200°C Physical

Range taken to represent bounds of

compartment flame temperatures [23,

24]. The base case is taken as the upper

end of the range to represent worst case

conditions and provide similarity to

earlier work [4].

Structural

Material

Concrete or

Steel Concrete Building

Two structure types have been

considered: concrete and steel. This paper

predominately focuses on concrete, but

some comparison is made for three steel

beams: unprotected, 60min fire rated, and

120min fire rated.

Table 5.2: Parameter values for the base case and ranges investigated.

Page 149: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

129

(a)

(b)

Figure 5.6: (a) Peak bay temperatures vs. fire size for ∆x = 0.2625m; (b) Time for bay rebar

temperatures to reach 400°C on a log scale for time.

300

350

400

450

500

550

600

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Pe

ak

Ba

y T

em

pe

ratu

re (o

C)

Fire Size

10

100

1000

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Tim

e t

o 4

00

oC

(min

)

Fire Area

Page 150: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

130

Fire sizes between 5% and 20% result in the largest bay temperatures (between 538

and 548°C) and thus are the most challenging for the structure. The maximum peak

bay temperature is 548°C for a 10% fire. Note that both a very small fire (2%) and a

very large fire (100%) result in the same peak bay temperature of 410°C. The smaller

fire sizes have long durations, but relatively low far field temperatures. The larger

fire sizes have higher far field temperatures, but for shorter durations. The

maximum rebar temperature found for the 10% fire size results from an optimum

heating balance between far field temperature and duration. These results are

similar to conclusions of work previously reported [4, 13].

Because the most challenging scenario is the 10% fire size, it is used as the base case

for the rest of this sensitivity study.

Figure 5.6b gives the time for bay temperatures to reach 400°C. A reference value of

400°C was selected for comparison of heating times as this was a bay rebar

temperature reached by all but the smallest fire size (1.25%). It shows that the larger

fire sizes reach this temperature more quickly than the smaller ones, even though

they ultimately do not reach the same peak temperature. Note, however, that the

time for the bay rebar to reach a specified temperature for a travelling fire is

dependent on the location of the bay relative to the fire’s path, i.e. the time of near

field arrival relative to the total burning duration. This is explored further in Section

5.5.4.

5.5.2 Grid Size

The grid size was varied in a series of cases to ensure that the number of nodes in

the discretisation scheme is high enough to properly resolve the dynamics of the

problem. The grid size has an impact on three parts of the methodology: the

resolution of the far field temperature in Eq. (5.4), the total burning duration in Eq.

(5.9), and the resolution of a bay (R# ∆I⁄ ). The impacts of these parameters are

explored below.

Page 151: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

131

Figure 5.7 shows the error of the peak bay temperature relative to the finest grid

against varying grid sizes. The finest grid size used for any calculation was 0.21m,

which is fine enough to include more than one node across the smallest fire size

(1%). The smaller the grid size, the lower the error, thus proving the grid

independence of the model. A grid size of 1.05m gives an error of approximately 1%

for several fire sizes, including the base case 10% fire size, and therefore has been

selected as the base case grid size.

Figure 5.7: Error in the peak bay temperature relative to finest grid (∆I = 0.21m) vs. grid

size for a range of fire sizes.

The evolution of the gas temperature and the resulting bay temperatures for the last

bay (Bay 6) at the far end of the structure (node n) are shown in Figure 5.8 for three

grid sizes: coarse (∆I = 10.5m), medium (∆I = 2.1m), and fine (∆I = 0.21m). For the

course grid, the peak bay temperature was lower (by 63°C, difference of 12.7%) and

arrived earlier (by 15min, difference of 15.6%) than for the fine grid which resulted

in a peak bay temperature of 514°C at 96min after ignition. The results of the

medium grid are very similar to the fine grid (517°C peak bay temperature at

0.01%

0.10%

1.00%

10.00%

0.1 1 10

Tem

pe

ratu

re E

rro

r

Δx (m)

5% Fire

10% Fire

25% Fire

75% Fire

Page 152: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

132

95min). Given the differences in structural heating resulting from the coarse and

fine grids, and the similarities of heating from the medium and fine grids, the model

is concluded to be grid independent for grid sizes of 2.1m and finer.

Figure 5.8: Gas phase and resulting bay temperatures vs. time at the far end of the

structure (Bay 6) for coarse (∆I = 10.5m), medium (∆I = 2.1m), and fine

(∆I = 0.21m) grids.

The change of slope in the gas phase curves at 19min is due to the growth of the fire

to its full size prior to that time. Note that these bay temperature results are for the

last bay in the compartment. Thus when the fire ends, the gas temperature returns

immediately to ambient. After that, the rebar is still heated from the thermal wave

passing through the slab but then slowly cools at a rate controlled by the heat

transfer in the concrete. This cooling phase and its relationship to whole frame

response during a fire are of great importance to structural engineering [33, 34, 35].

The more well resolved the compartment, the longer the total burning duration is,

eventually approaching "EFE�G∗ as can been seen from Eqs (5.9) and (5.10). For the gas

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Tem

pe

ratu

re (o

C)

Time (min)

Δx=10.5m gas

Δx=2.1m gas

Δx=0.21m gas

Δx=10.5m rebar

Δx=2.1m rebar

Δx=0.21m rebar

Δx = 2.1m

(gas phase)

Δx = 10.5m

(gas phase)

Δx = 0.21m

(gas phase)

Δx = 10.5m

(rebar)

Δx = 2.1m

(rebar)

Δx =0. 21m

(rebar)

Page 153: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

133

phase temperatures shown in Figure 5.8, "EFE�G is 80% of the theoretical limit, "EFE�G∗ ,

for the coarse grid ("EFE�G is 76min compared to "EFE�G∗ which is 95min), 96% for the

medium grid ("EFE�G of 91.2min), and 99.6% for the fine grid ("EFE�G of 94.6min). This

is one reason for the earlier and lower peak bay temperature seen for the coarse

grid. As an additional check on the impact of this fraction of the theoretical

maximum burning duration, one local burning time was added to the coarse grid

case (spread evenly amongst the three far field components of the gas phase

temperature-time curve), bringing "EFE�G to 95min and equal to "EFE�G∗ . The peak bay

temperature from this check was 477°C (7.5% lower than that from the finest grid) at

100min (4.2% later), instead of the previous 451°C peak and 15min time difference.

Thus, the impact of the temporal delay introduced by coarse grids can be easily

quantified.

Coarse grids that are on the same order of length as a structural bay could also

affect the bay temperatures. This is explored in Section 5.5.4.

5.5.3 Rebar Depth

The depth of rebar is a fundamental design variable for any concrete structure.

Typical rebar depths are between 20 and 60mm. A structural engineer would

usually establish the rebar depth of a structure before its fire performance is

analysed in detail. However, it is worth understanding the impact of rebar depth on

peak bay temperatures, as it could make a significant difference in the design and,

subsequently, the performance and cost of the structure.

Figure 5.9a shows the gas phase and resulting bay temperature vs. time for various

rebar depths for the base case. Figure 5.9b shows the peak bay rebar temperature for

varying rebar depth and fire size, for a grid size of 0.21m. The results show the

logical result that the shallower the rebar, the higher its temperature.

Page 154: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

134

(a)

(b)

Figure 5.9: (a) Gas phase and bay temperatures for rebar depths of 20, 30, 42 and 50mm;

(b) Peak bay temperature vs. fire area and rebar depth for ∆I = 0.21m.

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250

Tem

pe

ratu

re (o

C)

Time (min)

Gas Phase at Bay 6

20mm Rebar

30mm Rebar

42mm Rebar

50mm Rebar

Pe

ak

Ba

y T

em

pe

ratu

re (

oC

)

Page 155: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

135

The 10% fire size results in the maximum peak bay temperature for all rebar depths

except the 50mm depth, which has its maximum at the 5% fire size. This is due to

the increased importance of the pre-heating and post-heating of the rebar from the

far field, which is longer for smaller fires. A rebar depth of 42mm is used for the

base case as this was the design value for the similar structure in [4].

5.5.4 Bay Location and Bay Size

As discussed above, the bay temperature is a critical parameter for structural

response. Figure 5.10 shows the sensitivities of the bay location and bay size. Figure

5.10a gives the temperature-time curves for each bay in the compartment (see Figure

5.5 for bay numbering). Figure 5.10b gives the peak bay temperature as a function

bay length for three fire sizes (5%, 10%, and 25%). The fire begins in Bay 1 and

travels across the structure, eventually ending in Bay 6.

Figure 5.10a shows that the peak bay temperature increases with distance from the

ignition location. This is because the peak temperatures are always caused by

exposure to the near field, but are also dependent on the bay temperature at the

time of near field arrival. The bay temperature at the time the fire arrives is

dependent on the exposure duration and temperatures of the far field. As each

subsequent bay along the structure is exposed to longer pre-heating times prior to

the arrival of the near field, the hottest peak bay temperature is found in the final

bay (Bay 6).

This conclusion can be generalised, stating that the peak rebar temperature in a

structure will occur at the final burning location of the fire. This is a significant

result, as it means that the exact travel path of a fire does not need to be known if

the peak rebar temperature is the variable of interest for the structural analysis. This

is beneficial for design, as the path cannot be known a priori as there are many

possible paths of fire travel depending on ignition location, early fire development

and subsequent glazing failure.

Page 156: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

136

(a)

(b)

Figure 5.10: (a) Bay temperatures vs. time for each bay in the structure along its length;

(b) Variation of peak bay temperature with bay length for 5%, 10% and 25% fire

sizes.

0

100

200

300

400

500

600

0 50 100 150 200 250

Ba

y T

em

pe

ratu

re (o

C)

Time (min)

Bay 1

Bay 4 Bay 5 Bay 6

Bay 2Bay 3

400

440

480

520

560

600

0 5 10 15 20 25

Pe

ak

Ba

y T

em

pe

ratu

re (o

C)

Bay Length (m)

5% Fire

10% Fire

25% Fire

Page 157: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

137

Thus for design, if the structural engineer can identify particular areas of the

structure that are most vulnerable to the effects of elevated rebar temperature, then

it can be conservatively assumed that the fire reaches this location last, thereby

producing the most onerous fire environment for that part of the structure. Note

that other structural variables are important in travelling fires (see [4]) and that the

role played by the heating and cooling phases, for example, are not directly

captured by the peak bay temperature alone.

Figure 5.10b shows the impact of bay size on bay temperature. The bay size was

varied from 1.05m (the smallest possible bay size for the base case grid size, as there

is only a single node per bay) to 21m (half the length of the structure, which is

deemed to be beyond a realistic upper bound). The results indicate that the larger

the fire, the less impact the bay size has on the peak bay temperature. This is due to

the ratio between fire size and bay size. For bay sizes that are smaller than the fire

size, the full bay is exposed to the near field at once. Given that much of the range in

bay size variation is less than the fire size for the 25% case (the largest fire examined

here, with R� = 10.5m), little impact on peak temperatures is expected from variation

of bay size. However, for the smaller fire sizes, many of the bay lengths examined

are greater than the fire lengths (2.1m for the 5% fire and 4.2m for the 10%).

Therefore impact of bay size is to be expected in these cases.

The results also show that the maximum peak bay temperatures occur nearly, but

not exactly, when the bay size is equal to the fire size. This is due to the balance of

higher far field temperatures prior to the fire arriving and lower far field

temperatures after the fire passes. There is a small effect of the grid size on the peak

value, but as the temperature differences are small (on the order of 10°C) it is not

deemed significant.

Page 158: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

138

5.5.5 Fuel Load Density and Heat Release Rate per Unit Area

Eq. (5.2) gives the local burning time as a function of the fuel load density and heat

release rate per unit area. The local burning time, in turn, affects the total burning

duration. The higher the fuel load, the longer the local burning time and, thus, the

longer the total burning duration. The heat release rate per unit area also impacts

the burning times. The higher the heat release rate per unit area, the shorter the local

burning time and total burning duration of a fire. However, the heat release rate per

unit area also has an impact on the total heat release rate for a given fire size and,

therefore, the far field temperatures. This means that as it reduces the total fire

duration, it also increases the gas phase temperatures to which the structure is

exposed.

The amount of fuel in a building significantly alters the dynamics of a fire. The fuel

load varies greatly for building types and guidance exists to provide typical ranges

[2]. The base case fuel load was taken as the 80th percentile value for office buildings

[19]. The range of values for the sensitivity study varies from sparsely furnished

(classroom) to densely loaded (library) spaces according to [2]. The heat release rate

per unit area is a fundamental characteristic of a fire. The range selected here

corresponds to that measured for a variety of fuels that could be expected in a

typical office building [31], but excludes very high values that might be associated

with rack storage or other industrial usages. The base case value is taken from [20]

and is the same used in earlier work [4].

Figure 5.11 shows the variation of peak bay rebar temperature with fuel load

density for heat release rates per unit area of 200, 500, and 800kW/m2.

Denser fuel loads result in higher peak bay rebar temperatures. The opposite trend

is observed for the heat release rate per unit area, i.e. the lower the heat release rate

per unit area, the higher the peak bay rebar temperatures. Both of these trends can

be explained by the increase in time that results from in an increase in fuel load or

Page 159: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

139

decrease of the heat release rate per unit area. While the total heat release rate

increases for a higher heat release rate per unit area, these results suggest that the

effect of the reduction in fire duration is more important than the effect of the far

field temperature on the structural heating. This is due to the linear relationship

between heat release rate per unit area and time and the 2/3 power relationship

between heat release rate and far field temperature.

Figure 5.11: Peak bay temperature vs. fuel load density for a range of heat release rates per

unit area.

5.5.6 Heat Transfer

Because it is difficult to quantify specific values of the overall heat transfer

coefficient and emissivity in a fire, the sensitivity of these parameters has been

examined here. The convective heat transfer coefficient of the exposed side of the

concrete slab was varied from 10 to 100W/m2 K to represent the bounds typically

expected in a compartment fire [48]. The material emissivity was varied from 0.2 to

1. For typical concrete reradiation at high temperatures, the effective emissivity is

likely to be high, but 0.2 has been examined as a lower bound. The gases are

350

400

450

500

550

600

650

700

750

0 200 400 600 800 1000 1200 1400 1600

Pe

ak

Ba

y T

em

pe

ratu

re (o

C)

Fuel Load Density (MJ/m²)

200 kW/m²

500 kW/m²

800 kW/m²

Page 160: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

140

assumed to have an emissivity equal to 1, and the material absorptivity is assumed

to be equal to the emissivity. The base case values of both heat transfer parameters

were taken according to Eurocode 1 guidance [2].

Figure 5.12 plots peak bay temperature against the convective heat transfer

coefficient for varying values of emissivity and two rebar depths. A shallow rebar

depth (20mm) was examined, in addition to the base case value, to include a

scenario of reduced importance of the conductive heat transfer.

Figure 5.12: Peak bay temperature vs. convective heat transfer coefficient for a range of

material emissivities and rebar depths.

The results indicate that the peak bay temperatures are only marginally affected by

the heat transfer parameters at either of the two rebar depths studied. The lower

temperatures that result from the lower emissivities indicate that concrete heating is

dominated by radiation in the base case.

400

500

600

700

800

900

0 20 40 60 80 100

Pe

ak

Ba

y T

em

pe

ratu

re (o

C)

Convective Heat Transfer Coefficient (W/m²K)

ε=0.2, 42mm rebar

ε=0.5, 42mm rebar

ε=0.7, 42mm rebar

ε=1, 42mm rebar

ε=0.2, 20mm rebar

ε=0.5, 20mm rebar

ε=0.7, 20mm rebar

ε=1, 20mm rebar

Page 161: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

141

5.5.7 Near Field Temperature

For the sake of conservatism, the methodology assumes that the near field

temperature is the peak flame temperature measured in large fires. The sensitivity

of bay temperatures to this assumption is studied here. Peak temperatures in small

fires have been measured in the range of 800 to 1000°C [23], while those in larger

compartments have been found to be up to approximately 1200°C [24]. The FDS

simulations of a localised 147MW fire in a large compartment shown in Figure 5.3

agree with this range and predict peak near field temperatures ranging from 800 to

1050°C, depending on the ventilation scenario. Therefore the near field temperature

has been varied from 800 to 1200°C, with the base case value at the upper end of the

range to account for worst case conditions and overcome the uncertainty associated

with the prediction and measurement of flame temperatures. Figure 5.13 shows the

bay temperature evolution over time for varying near field temperatures at Bays 2

and 6.

Figure 5.13: Bay temperature vs. time for near field temperatures between 800 and 1200°C at

Bays 2 and 6.

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

Ba

y T

em

pe

ratu

re (o

C)

Time (min)

800°C Bay 6

900°C Bay 6

1000°C Bay 6

1100°C Bay 6

1200°C Bay 6

800°C Bay 2

900°C Bay 2

1000°C Bay 2

1100°C Bay 2

1200°C Bay 2

Bay 2

Bay 6

Page 162: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

142

The results show that a near field temperature variation of 400°C (from 800 to

1200°C) produces a peak bay temperature range of approximately 130°C. The results

are similar for both bays. The near field temperature assumed has no impact on the

structural heating in the far field region, but does have an important overall effect

on the predicted fire resistance of the structure. However, given that the design

value is taken at the upper end of the physical range, it means results from this

methodology can be deemed conservative.

5.5.8 Steel Structure

In addition to the base case concrete structure, the heating of a typical steel beam is

also examined. The steel beam studied was selected to be representative of typical

section sizes used in real buildings. Dimensions of the beam are given in Figure

5.14. The beam has been assessed with three levels of fire protection: unprotected,

fire rated to 60min, and fire rated to 120min. For quantification of its heating, it is

assumed that there is a slab above the top flange of the beam and thus it is only

heated on three sides.

Figure 5.14: Dimensions of the steel beam section analysed.

The heat transfer to the beam was calculated utilising a lumped mass approach and

is given in Appendix A. For the purposes of this analysis, it is assumed that the steel

beam is perpendicular to the direction of fire propagation and thus is exposed to the

same gas temperature along its full length at any given time. This is done because

15mm

15mm

8mm

200mm

350mm

Not to scale

Page 163: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

143

using a single beam temperature as a surrogate for structural response is not valid

for a beam exposed to a varying temperature along its length. This methodology

could also be used for calculation of the distribution of steel temperatures along the

beam axis as the rate of conductive heat transfer in steel is much lower than the

spread rate of a travelling fire. However determining the structural response of that

scenario would require the adoption of a two or three-dimensional structural

analysis method. Nonetheless, the single point heat transfer calculations used here

provide insight into the differences in heating of the three types of steel beam, as

compared to the concrete slab.

Figure 5.15a shows the resultant peak steel temperatures for the three beam types at

the far end of the final structural bay (Bay 6) for a grid size of 0.21m. The fine grid

resolution was used to best match the node size to the physical size of the steel

beam.

It can be seen that the steel temperatures of the unprotected beam reach the near

field temperature for all fire sizes. This is due to the low thermal inertia and high

conductivity of the unprotected steel. The protected beam temperatures follow a

similar trend to that of the concrete structure. The maximum temperature recorded

for the 60min rated beam is from a 10% fire size and for the 120min beam from a 5%

fire size.

Figure 5.15b gives the time for the unprotected and 60min rated beams to reach

550°C (the 120min rated beams do not reach this temperature and are therefore not

shown). A critical value of 550°C was selected here as this is normally considered an

approximate temperature above which steel loses sufficient strength such that

failure of a typical simply-supported beam could occur under the loads assumed to

be applied during a fire [24]. As with the concrete bay temperatures, it shows that

the larger fire sizes reach the specified temperature more quickly than the smaller

ones, even though they ultimately do not reach the same peak temperature.

Page 164: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

144

(a)

(b)

Figure 5.15: (a) Peak steel temperature vs. fire size for unprotected, 60min rated, and 120min

rated steel beams at the far end of Bay 6 for a grid size of ∆I = 0.21m; (b) Time

for the unprotected and 60min rated steel beams to reach 550°C on log scale for

time.

0

200

400

600

800

1000

1200

1400

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ste

el T

em

pe

ratu

re (o

C)

Fire Size

Unprotected

60min

120min

10

100

1000

10000

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Tim

e t

o 5

50

oC

(min

)

Fire Area

Unprotected

60min

Page 165: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

145

The unprotected beam reaches 550°C between 29min (for the 1% fire) and 34min (for

the 50% fire) faster than the 60min rated beam. Fire sizes above 50% do not reach

550°C for the 60min rated beam. Note, however, as with the concrete rebar heating,

the time for the steel beam to reach a specified temperature for a travelling fire is

dependent on the location of the bay relative to the fire’s path, i.e. the time of near

field arrival relative to the total burning duration.

Figure 5.16 shows temperature-time curves for the gas phase and steel for all three

beam types considered at two different locations in the structure. The unprotected

steel temperature follows the gas phase temperature very closely, for the reasons

given above. The peak steel temperatures are very similar for both locations, with a

slightly higher peak reached for the midpoint of Bay 2 for the 60min rated beam.

This lack of sensitivity to steel location is different from that observed in concrete

(see Figure 5.10a)

Figure 5.16: Temperature vs. time for the gas phase plus all three steel beam types at the

midpoint of Bay 2 and the far end of Bay 6.

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300

Tem

pe

ratu

re (o

C)

Time (min)

Bay 6, Gas

Bay 2, Gas

Bay 6, Unprotected Steel

Bay 2, Unprotected Steel

Bay 6, 60min Steel

Bay 2, 60min Steel

Bay 6, 120min Steel

Bay 2, 120min Steel

Midpoint

of Bay 2

End of

Bay 6

Page 166: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

146

5.6 Comparison to Conventional Methods

Figure 5.17 compares the bay temperature-time curves resulting from the base case

fire scenario with those calculated from the standard fire and two Eurocode

parametric temperature-time curves [2]. One parametric temperature-time curve

assumes 100% glass breakage on the façade and the other 25%. The parametric

curves use the same thermal properties of concrete (see Appendix A for values) and

fuel load density as the base case.

Figure 5.17: Comparison of bay temperatures calculated using the base case, the standard

fire, and two Eurocode parametric temperature-time curves.

The comparison shows that the base case, which is the most onerous fire size in the

family of fires, is a more challenging scenario for the structure in terms of peak bay

temperature reached than the two parametric curves. In terms of the peak bay

temperature, the travelling fire is equivalent to 106min of the standard fire, which is

similar to the conclusions of Law et al. [4]. This is compared to the two parametric

curves, which are equivalent to 38min and 56min of the standard fire.

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250

Ba

y T

em

pe

ratu

re (o

C)

Time (min)

Base Case

EC - 25% Ventilation

EC - 100% Ventilation

Standard Fire

Base case equivalent to

106 min Standard Fire

106 min

556oC

56 min38 min

363oC

252oC

Page 167: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

147

The results presented here should be explored in more detail by a structural

engineer, as a travelling fire may lead to different structural behaviour than that

indicated by examining the peak bay temperature alone [4]. For example, whole

frame behaviour resulting from exposure to a travelling fire with portions of the

structure being heated while other areas are cooling may be different than that

suggested by the bay average results given here.

5.7 Final Remarks

Comparisons of the relative impact of all the parameters varied in the methodology

are shown in Figure 5.18. The percentage variation of each parameter from the

corresponding base case value has been plotted against the resultant percentage

change of the peak bay temperature calculated. Figure 5.18a shows the results for

the building parameters, and Figure 5.18b the physical and numerical parameters.

Fire size has been shown on both plots as it is the main variable in this

methodology.

Steeper slopes on the curves in Figure 5.18 correspond to the more sensitive

parameters. Positive values in the bay temperature change mean conditions are

more onerous on the structure than the base case and negative values less onerous.

The largest changes in bay temperature come from rebar depth, fuel load density,

fire size, and near field temperature, in this order. These are the most sensitive

parameters.

Page 168: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

148

(a)

(b)

Figure 5.18: Relative change in bay temperature vs. percentage change in (a) building

parameters and; (b) physical and numerical parameters.

-35%

-25%

-15%

-5%

5%

15%

25%

35%

45%

-100% -50% 0% 50% 100% 150% 200% 250% 300%

Re

lati

ve

Ba

y T

em

pe

ratu

re C

ha

ng

e

Percentage Change from Base Case Value

Building Parameters

Fire Size

Rebar Depth

Fuel Load

Bay Size

-35%

-25%

-15%

-5%

5%

15%

25%

35%

45%

-100% -50% 0% 50% 100% 150% 200% 250% 300%

Re

lati

ve

Ba

y T

em

pe

ratu

re C

ha

ng

e

Percentage Change from Base Case Value

Physical and Numerical Parameters

Fire Size

Grid Size

Emissivity

Conv HT Coeff

Tnf (Concrete)

Page 169: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

149

The rebar depth, the most sensitive parameter, is likely to be a fixed value early in

the design, but its sensitivity is worth noting for the design process of a building.

The exact fuel load density cannot be known exactly, as it is inherently variable and

may change over the lifetime of a building. Therefore a reasonable assessment of the

likely values should be made during design. It is noted that both of these

parameters would be used by many forms of structural fire assessment, whether

that be the travelling fires methodology presented in this paper or the conventional

methods.

Fire size is the main variable of this methodology, so the full range should always be

explored in a design case. While the near field temperature has a marked impact on

the bay temperatures, it is not necessary to vary this parameter for design, as the

methodology assumes the most onerous condition.

The methodology presented in this paper offers a paradigm shift in defining fire

scenarios for structural fire engineering and compliments the traditional methods.

This paper has explored the details of the method and concluded on the more

sensitive parameters that ought to be considered in design. The methodology

provides a robust platform for collaboration between fire engineers and structural

fire engineers to jointly understand a building’s structural performance in fire.

References

1 Babrauskas, V. and Williamson R.B., “The historical basis of fire resistance

testing – Part II.” Fire Technology, 14(4) 1978, pp. 304-316.

2 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on

structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.

3 Stern-Gottfried, J., Chapter 3 in: Travelling Fires for Structural Design, PhD Thesis,

School of Engineering, University of Edinburgh, 2011.

Page 170: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

150

4 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “The influence of travelling

fires on a concrete frame”, Engineering Structures, Vol. 33, 2011, pp. 1635-1642.

doi:10.1016/j.engstruct.2011.01.034. Open access version at:

http://www.era.lib.ed.ac.uk/handle/1842/4907

5 Jonsdottir, A. and Rein, G. “Out of Range”, Fire Risk Management, Dec 2009, pp.

14-17. http://www.era.lib.ed.ac.uk/handle/1842/3204

6 Gann, R.G. et al, “Reconstruction of the Fires in the World Trade Center

Towers”, NIST NCSTAR 1-5, September 2005.

7 McAllister, T.P. et al, “Structural Fire Response and Probably Collapse Sequence

of the World Trade Center Building 7”, NIST NCSTAR 1-9, November 2008.

8 Fletcher, I. et al, “Model-Based Analysis of a Concrete Building Subjected to

Fire,” Advanced Research Workshop on Fire Computer Modelling, Santander, Spain,

2007.

9 Zannoni, M. et al, “Brand bij Bouwkunde”, COT Instituut voor Veilingheids – en

Crisismanagement, December 2008.

10 Thomas, I.R. and Bennets, I.D., “Fires in Enclosures with Single Ventilation

Openings – Comparison of Long and Wide Enclosures”, The 6th International

Symposium on Fire Safety Science, Poitiers, France, 1999.

11 Kirby, B.R. , Wainman, D. E., Tomlinson, L. N., Kay, T. R., and Peacock, B. N.,

“Natural Fires in Large Scale Compartments”, British Steel, 1994.

12 Stern-Gottfried, J., Rein, G., Bisby, L.A., Torero, J.L., “Experimental review of

the homogeneous temperature assumption in post-flashover compartment

fires”. Fire Safety Journal, 45, 2010, pp. 249-261.

http://www.era.lib.ed.ac.uk/handle/1842/3866

13 Jonsdottir, A.M., Stern-Gottfried, J., Rein, G., “Comparison of Resultant Steel

Temperatures using Travelling Fires and Traditional Methods: Case Study for

the Informatics Forum Building”. The 12th International Interflam Conference.

Nottingham, UK, 2010.

Page 171: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

151

14 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,

The 9th International Symposium on Fire Safety Science. Karlsruhe, Germany, 2008.

15 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and

Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th

International Symposium on Fire Safety Science, University of Maryland, USA,

2011.

16 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern

Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra

Incêndio, Natal, Brazil, 2011.

17 Rein, G. et al, “Multi-story Fire Analysis for High-Rise Buildings,” The 11th

International Interflam Conference, London, UK 2007.

http://www.era.lib.ed.ac.uk/handle/1842/1980

18 Stern-Gottfried, J., Rein, G., Lane, B., and Torero, J. L., “An innovative approach

to design fires for structural analysis of non-conventional buildings: A case

study,” Application of Structural Fire Engineering, Prague, Czech Republic, 2009,

http://eurofiredesign.fsv.cvut.cz/Proceedings/1st_session.pdf

19 PD 6688-1-2:2007, Background Paper to the UK National Annex to BS EN 1991-

1-2.

20 TM19, “Relationships for Smoke Control”, CIBSE, 1995

21 Walton, W.D. and Thomas, P.H., "Estimating Temperatures in Compartment

Fires", Chapter 3-6 of the SFPE Handbook of Fire Protection Engineering, 3rd Edition,

2002.

22 Harmathy, T.Z., “A New Look at Compartment Fires, Part II”, Fire Technology,

Vol. 8 No. 4, 1972, pp.326-351, doi:10.1007/BF02590537.

23 Audoin, L., Kolb, G., Torero, J.L., and Most, J.M.. “Average centreline

temperatures of a buoyant pool fire obtained by image processing of video

recordings”, Fire Safety Journal, Vol. 24, 1995, pp. 167-187. doi:10.1016/0379-

7112(95)00021-K.

Page 172: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

152

24 Drysdale, D., An Introduction to Fire Dynamics, 2nd Edition, John Wiley & Sons,

1999.

25 Heskestad, G., “Fire Plumes, Flame Height, and Air Entrainment”, Chapter 2-1 of

the SFPE Handbook of Fire Protection Engineering, 3rd Edition, 2002.

26 Alpert, R.L., “Calculation of Response Time of Ceiling-Mounted Fire Detectors”,

Fire Technology, Vol. 8, 1972, pp. 181–195.

27 Alpert, R.L., “Ceiling Jet Flows”, Chapter 2-2 of the SFPE Handbook of Fire

Protection Engineering, 3rd Edition, 2002.

28 Clifton, G.C., “Fire Models for Large Firecells”, HERA Report R4-83, 1996, with

proposed changes in HERA Steel Design and Construction Bulletin Issue No 54,

February 2000 and updates to referenced documents, September 2008.

29 Routley, J.G., Jennings, C., and Chubb, M., “Highrise Office Building Fire, One

Meridian Plaza, Philadelphia, Pennsylvania”, U.S. Fire Administration

Technical Report 049.

30 Quintiere, J.G, “Surface Spread of Flame”, Chapter 2-12 of the SFPE Handbook of

Fire Protection Engineering, 3rd Edition, 2002.

31 Karlsson, B., and Quintiere, J.G., Enclosure Fire Dynamics. CRC Press, 1999.

32 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, School of

Engineering, The University of Edinburgh, 2006,

http://www.era.lib.ed.ac.uk/handle/1842/1480.

33 Bailey, C.G., Burgess, I.W., and Plank, R.J., “Analyses of the Effects of Cooling

and Fire Spread on Steel-framed Buildings”. Fire Safety Journal, Vol. 26, 1996, pp.

273-293.

34 El Rimawi, J.A., Burgess, I.W., and Plank, R.J., “The Treatment of Strain

Reversal in Structural Members during the Cooling Phase of a Fire”. Journal of

Constructional Steel Research, Vol. 37, 1996, p115-135.

35 Röben, C., The effect of cooling and non-uniform fires on structural behaviour. PhD

thesis, School of Engineering, The University of Edinburgh, 2006.

Page 173: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

153

6 Conclusions and Future Work

6.1 Conclusions

Most fire tests that have been used in the development of traditional tools to define

the thermal environment for structural fire design had floor areas on the order of

only a few square metres. Larger tests, which are far fewer in number, extend to

floor areas on the order of one hundred square metres. Given that floor to ceiling

heights of real buildings are typically only a few metres regardless of floor area, the

relative impact of a compartment’s walls on the heat transfer with hot fire gases is

greatly reduced in larger compartments. In addition it is well known that radiation,

which governs flame spread in compartment fires, does not scale well. Therefore

applying data that are extrapolated from small compartment tests to large buildings

is inappropriate and has led to design methods that do not replicate real fire

behaviour at that scale.

Page 174: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

154

One common conclusion from these small scale tests that is manifest in the

traditional structural fire design methods is that of a uniform gas phase

temperature. This homogeneous temperature assumption has been reviewed in

Chapter 2. It is shown that this assumption does not hold well. The temperature

heterogeneity that actually exists in real compartment fires does have an impact on

the heating of a structure.

However, conducting fire tests in enclosures of a size of interest for modern

building design (floor plates on the order of thousands of metres squared) is

difficult and costly. Therefore practical solutions to characterising fire behaviour in

large enclosures are needed. To this end, this thesis has developed a methodology to

characterise travelling fires for structural design. The approach used is a dramatic

departure from the traditional methods and suggests a paradigm shift in structural

fire engineering. It has been shown that this methodology both addresses

limitations in the existing methods and enables innovation in design by providing a

more realistic characterisation of the fire environment of a building.

The methodology, which is presented in Chapters 3, 4 and 5, addresses the lack of

large scale test data by examining a full range of fire sizes rather than trying to

calculate one. This fits well with the uncertainty associated in fire growth and

development in large, real buildings. The family of fires approach ensures that the

most challenging, physically possible fire scenario is considered for structural

design.

Each member of the family of fires produces far field temperatures and burning

durations related to its size. Large fires have high far field temperatures but short

durations, while small fires have low far field temperatures and long durations. The

application of the travelling fire methodology has shown that medium sized fires

(10% to 25% of the floor area) prove most challenging to a generic concrete

Page 175: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

155

structure. These fire sizes have an optimum balance of elevated far field

temperatures and total fire duration.

The sensitivity studies conducted in Chapters 4 and 5 give insight into the effect of

varying the methodology’s input parameters. It has been shown that the most

sensitive parameters are related to the building design and use and not the

theoretical or numerical formulation of the approach. This enables practical

application of the methodology in design without the need for cumbersome

sensitivity studies of every parameter.

Accurately calculating the behaviour of a structure exposed to fire is necessary for

performance based design. However, quantifying the thermal environment created

by a fire, the resultant heating of the building elements, and the subsequent

structural response requires a broad set of skills from disparate engineering

disciplines. Therefore it has been recognised that no one individual should do this

alone and fire engineers should work with structural fire engineers to jointly solve

this problem [1, 2].

This is the spirit in which the methodology presented in this thesis has been

developed. Chapter 4 provides a good example of collaborative work between fire

and structural fire engineers. However, further collaboration is needed to better

understand the impact of travelling fires on structural performance. The travelling

fires methodology provides a robust platform for this collaborative research.

6.2 Future Work

While the travelling fires methodology developed in this thesis provides a practical

tool that can be used in design, as shown by the case studies and sensitivity analyses

in Chapters 4 and 5, further research would serve to improve it and make it more

robust.

Page 176: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

156

6.2.1 Fire Environment

Often large scale tests in structural fire research aim to create uniform fire

conditions by providing multiple ignition points throughout evenly distributed fuel

packages. These tests also tend to be sparsely instrumented to collect data in the gas

phase. Conducting large scale tests in real buildings could greatly serve to increase

understanding of the dynamics of travelling fires. These tests should allow the fire

to grow and travel on its own and be well instrumented so the far field

temperatures and fire movement could be recorded.

Far field temperatures in this thesis have been calculated by means of an empirical

ceiling jet correlation. It has been noted that the use of this correlation is a simple

solution to a complex problem. The correlation provides temperatures as a function

of distance from the fire, but can only be applied in limited geometries.

Computational Fluid Dynamics (CFD) was used in the earliest version of the

travelling fires methodology [3] and is more readily applicable to complex

geometry; however it has drawbacks related to complexity and computational

effort. The lack of large scale test data means it is difficult to validate both the

simplistic correlations and CFD approaches taken. Work to develop better

engineering tools to calculate the far field temperature would benefit the

methodology. Such tools should consider the open nature of large, modern

compartments and not automatically assume the fires are ventilation limited [4].

On potential compromise between the correlation and CFD could be to solve the

Laplace Equation (∇+s = 0). The solution to this transport equation could be viewed

as an analogue of smoke movement. This approach, which is illustrated in Figure

5.11 for a generic structure similar to those used in Chapters 4 and 5, could explore

more complex geometry than the ceiling jet correlation, but in much less calculation

time than CFD. A Dirichlet boundary condition could represent flow out of an open

window and a Neumann boundary condition flow next to a solid wall.

Page 177: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

157

(a) (b)

Figure 6.1: Illustration of a solution of the Laplace Equation in a generic concrete structure

showing (a) 3D contours and; (b) streamlines in plan view.

The travelling fires methodology has, to date, only focussed on horizontally

travelling fires. However, as noted in Chapter 3, accidental fires do travel vertically

as well. The sole study on the structural impact of vertically travelling fires [5], only

considers uniform fires on each floor. The methodology presented in this thesis

could be applied to vertically travelling fires as well. The time delay of spread from

one floor to the next would need to be parametrically varied. Care would need to be

taken to combine a range of such time delays with various fire sizes to ensure the

most onerous design case is identified.

6.2.2 Fire – Structure Interface

The traditional methods used in defining the thermal environment for structural fire

engineering specify gas phase temperature-time curves. The subsequent heat

transfer calculations utilise these curves to calculate the structural temperature

evolution. It was actively decided to produce gas phase temperature-time curves as

the output of the travelling fires methodology to conform to the existing heat

transfer methods used by the structural fire community. However, it is noted that

Fire

Core

x (m

)

y (m)

Re

lati

ve

Te

mp

era

ture

Ris

e (

-)

Page 178: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

158

the actual heating of a structure results from the net heat flux to it, rather than solely

the exposure temperature. Calculation of the heat flux from a fire to a structural

element is a complex process and requires knowledge of smoke conditions such as

velocity, soot content, and layer depth. Methods have been developed to examine

this [6, 7], but this concept should be explored in relation to travelling fires.

6.2.3 Structural Response

The travelling fires methodology provides a powerful tool for structural fire

research. In collaboration with fire engineers, this methodology enables structural

engineers to examine more realistic structural response to fire than the traditional

methods. Construction types other than the concrete frame examined in Chapters 4

and 5 should be examined with this approach. Composite steel–concrete

construction is of particular interest due to its prevalence in the built environment.

A central concept of travelling fires is the non-uniform temperature field. The

impact of this on the full frame behaviour of structures should be explored.

Additionally, some structures may be more vulnerable to severe near field

conditions than others, such as post-tensioned concrete slabs. The traditional

methods do to not generally consider local near field conditions, so this should be

researched.

Small travelling fires also result in total fire durations much longer than those

calculated by the traditional methods. Thus a structure could be exposed to far field

temperatures of several hundred degrees Celsius for many hours. This could have a

significant impact on creep in steel structures and spalling in concrete frames.

Most importantly, however, the travelling fires methodology provides a framework

that allows fire engineers and structural fire engineers to jointly determine a

building’s true response in fire, thereby enabling architectural innovation and

structural optimisation.

Page 179: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

159

References

1 Buchanan, A., “The Challenges of Predicting Structural Performance in Fires”,

The 9th International Symposium on Fire Safety Science, Karlsruhe, Germany, 2008.

2 Law, A., Stern-Gottfried, J., Gillie, M., and Rein, G., “Structural Engineering and

Fire Dynamics: Advances at the Interface and Buchanan’s Challenge”, The 10th

International Symposium on Fire Safety Science, University of Maryland, USA,

2011.

3 Rein, G., Zhang, X., Williams, P., Hume, B., Heise, A., Jowsey, A., Lane, B., and

Torero, J.L. “Multi-story Fire Analysis for High-Rise Buildings”, The 11th

International Interflam Conference, London, UK, 2007.

http://www.era.lib.ed.ac.uk/handle/1842/1980

4 Majdalani, A.H. and Torero, J.L., “Compartment Fire Analysis for Modern

Infrastructure”, 1º Congresso Ibero-Latino-Americano sobre Segurança contra

Incêndio, Natal, Brazil, 2011.

5 Röben, C., Gillie, M., and Torero, J.L., “Structural behaviour of during a

vertically travelling fire”, Journal of Constructional Steel Research, Vol. 66, 2010,

pp. 191-197.

6 Jowsey, A., Fire Imposed Heat Fluxes for Structural Analysis. PhD thesis, School of

Engineering, The University of Edinburgh, 2006,

http://www.era.lib.ed.ac.uk/handle/1842/1480.

7 Prasad, K. and Baum, H., “Fire Structure Interface and Thermal Response of the

World Trade Center Towers”, NIST NCSTAR 1-5G, September 2008.

Page 180: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

160

Page 181: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

161

Appendix

Page 182: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

162

Page 183: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

163

A Heat Transfer Calculations

This appendix provides the details of the simplified heat transfer calculations used

to quantify the rebar and steel temperatures used in Chapters 2 and 5 of this thesis.

A.1 Concrete Temperature

To determine the in-depth temperature of the concrete, a one-dimensional finite-

difference approach to the heat conduction equation was taken in explicit form, as

given by Incropera et al. [1]. It is assumed that the rebar of the concrete is the same

temperature as the adjacent concrete.

The formulation from Incropera et al. only includes surface convection, so a

radiative term was added for the surface nodes. This gives Eq. (A.1) for calculating

the exposed surface node temperature, and Eq. (A.2) for the interior nodes, and Eq.

(A.3) for the backside surface node. Chapter 2 did not use Eq. (A.3), but rather

Page 184: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

164

assumed a sufficient depth of slab above the concrete beam such that the boundary

condition did not influence the results.

gEt: = 2∆"uKJK∆v wℎg� − gE� + �o x 4 − gE4y + zK∆v 2:E − gE3{ + gE (A.1)

bEt: = |}�bt:E + bM:E � + 21 − 2|}3bE (A.2)

/Et: = 2∆"uKJK∆v wℎ/2∞ − /E3 + �o x∞

4 − /E4y + zK∆v 2/M:E − /E3{ + /E (A.3)

where bE is the concrete temperature at time t, and location i (K) – a subscript of 0

indicates the exposed surface and a subscript of � the backside surface.

is the gas temperature (K)

. is the ambient temperature (293K)

uK is the density of concrete (2300kg/m3)

JK is the specific heat of concrete (1000J/kg K)

ℎ is the convective heat transfer coefficient (25W/m2 K for exposed surface in

Chapter 2, 35W/m2 K for the exposed surface and 4W/m2 K for the

backside surface in Chapter 5 [2])

� is the Stefan-Boltzmann constant (5.67x10-8W/m2 K4)

o is the radiative and reradiative emissivity of the material and gas

combined (assumed to be unity in Chapter 2, varied in Chapter 5)

zK is the thermal conductivity of concrete (1.3W/m K)

∆" is the time step (0.5s in Chapter 2, 10s in Chapter 5)

∆v is the element length (0.001m in Chapter 2, 0.01m in Chapter 5)

|} is the Fourier number (-), given in Eq. (A.4)

|} = zK∆"uKJK∆v+ (A.4)

Page 185: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

165

The time step and element length were selected to meet the stability criteria

highlighted by Incropera et al. The concrete material properties were taken from

Buchanan [3] for calcareous concrete.

A.2 Unprotected Steel Beam Temperature

The unprotected steel beam temperatures were calculated by a lumped mass heat

transfer method, as given by Buchanan [3], and shown below.

∆~ = -��1

u~J~ �ℎK� − ~� + �o� 4 − ~4��∆" (A.5)

where ~ is the steel temperature (K)

is the gas temperature (K)

-� is the heated perimeter of the beam (1.284m)

� is the cross section of the beam (0.00856m2)

u~ is the density of steel (7850kg/m3)

J~ is the temperature dependent specific heat of steel (J/kg K)

ℎK is the convective heat transfer coefficient (25W/m2 K in Chapter 2,

35W/m2 K in Chapter 5)

� is the Stefan-Boltzmann constant (5.67x10-8W/m2 K4)

o is the radiative and reradiative emissivity of the material and gas

combined (assumed to be unity in Chapter 2 and 0.7 in Chapter 5)

∆" is the time step (1s in Chapter 2, 10s in Chapter 5)

All constants and steel material properties (except the emissivity) are taken from

Buchanan, including the temperature dependent specific heat.

Page 186: Stern-Gottfried - Travelling Fires for Structural Design€¦ · Stern-Gottfried under the supervision of Dr Guillermo Rein and Prof José Luis Torero. Where others have contributed

166

A.3 Protected Steel Beam Temperature

The protected beam temperature calculation was also taken from Buchanan [3] and

is given below.

∆~ = -��zb5bu~J~

u~J~�u~J~ + �-� �⁄ � 5bubJb �⁄ � � − ~�∆" (A.6)

where zb is the thermal conductivity of the insulation (0.12W/m K)

5b is the thickness of the insulation (m)

ub is the density of the insulation (550kg/m3)

Jb is the specific heat of the insulation (1200J/kg K)

The material properties of the insulation were based on high density perlite, as

given by Buchanan. The thickness of the insulation was solved for using Eq. (A.6),

applying the standard temperature-time curve and limiting the steel temperature to

below 550°C for 60 and 120 minutes. This method should ensure a similar level of

performance for any insulating material used to achieve these fire ratings.

References

1 Incropera, F., DeWitt, D., Bergman, T., and Lavine, A., Fundamentals of Heat and

Mass Transfer, John Wiley & Sons, 2007.

2 Eurocode 1: Actions on structures – Part 1-2: General actions – Actions on

structures exposed to fire, European standard EN 1991-1-2, 2002. CEN, Brussels.

3 Buchanan, A., Structural Design for Fire Safety. John Wiley & Sons, 2002.